Free Printable EXTRA PRACTICE: Units 1 and 2

1.

What are the factors of
$x^2+5x+4$

a)

$\left(x+2\right)\left(x+3\right)$

b)

$\left(x-1\right)\left(x-4\right)$

c)

$\left(x-1\right)\left(x+5\right)$

d)

$\left(x+1\right)\left(x+4\right)$

2.

What are the factors of
$2x^2+5x-12$

a)

$\left(x+4\right)\left(2x-3\right)$

b)

$\left(x-3\right)\left(x+8\right)$

c)

$\left(2x+1\right)\left(x-12\right)$

d)

$\left(2x+3\right)\left(x-8\right)$

3.

What are the factors of
$4m^2-25$

a)

$\left(4m-5\right)\left(4m+5\right)$

b)

$\left(2m-5\right)\left(2m+5\right)$

c)

$\left(2m-10\right)\left(2m-15\right)$

d)

$\left(4m-1\right)\left(m-24\right)$

4.

What are the factors of
$3p^2-7p-6$

a)

$\left(p+3\right)\left(3p-2\right)$

b)

$\left(p+2\right)\left(p-9\right)$

c)

$\left(3p+2\right)\left(p-3\right)$

d)

$\left(3p-9\right)\left(3p+2\right)$

5.

What are the factors of
$5b^2-11b+2$

a)

$\left(5b-1\right)\left(b-2\right)$

b)

$\left(b-1\right)\left(b-10\right)$

c)

$\left(b-2\right)\left(b-5\right)$

d)

$\left(5b-2\right)\left(b-5\right)$

6.

What are the factors of
$8g^2-18g-5$

a)

$\left(g+2\right)\left(g-20\right)$

b)

$\left(8g-1\right)\left(g+5\right)$

c)

$\left(2g+1\right)\left(4g-5\right)$

d)

$\left(4g+1\right)\left(2g-5\right)$

7.

What are the factors of
$2n^2+12n+16$

a)

$2\left(n+1\right)\left(n+8\right)$

b)

$\left(2n+2\right)\left(n+8\right)$

c)

$2\left(n+2\right)\left(n+4\right)$

d)

$\left(n+16\right)\left(2n+1\right)$

8.

What are the factors of
$49x^2-100$

a)

$\left(7x-10\right)\left(7x+10\right)$

b)

$\left(x-4\right)\left(x-25\right)$

c)

$\left(x+10\right)\left(x-10\right)$

d)

$\left(49x-10\right)\left(x+10\right)$

9.

The area of a rectangular painting is $2x^2+13x-7$ units. Which of the following could be the dimensions of the painting?
*Hint: Factor the trinomial*

a)

$\left(2x+1\right)$ units by $\left(2x+7\right)$ units

b)

$\left(x-1\right)$ units by $\left(x+14\right)$ units

c)

$\left(x+1\right)$ units by $\left(2x+7\right)$ units

d)

$\left(2x-1\right)$ units by $\left(x+7\right)$ units

10.

Which binomial is a factor of
$9x^2-25$

a)

$\left(x+5\right)$

b)

$\left(3x-25\right)$

c)

$\left(9x-5\right)$

d)

$\left(3x+5\right)$

11.

Which binomial is a factor of
$3k^2+16k-12$ ?

a)

$\left(3k-2\right)$

b)

$\left(k+18\right)$

c)

$\left(k-6\right)$

d)

$\left(3k-6\right)$

12.

Which expression is a factor of
$x^2-3x-28$

a)

$\left(x+7\right)$

b)

$\left(x-4\right)$

c)

$\left(x-7\right)$

d)

$\left(x-3\right)$

13.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

14.

Factor 8x³ + 18x.

a)

2x(4x² + 9)

b)

8x(x² + 10)

c)

2(4x³ + 9x)

d)

8(x³ + 10x)

15.

Factor
3x⁴- 12xy

a)

x(3x³-12y)

b)

3x(x³- 4y)

16.

Factor 4b⁵ + 4b³ + 16b².

a)

4b²(b³ + b + 4)

b)

4(b⁵ + b³ + 4b²)

c)

4b³(b⁴ + 4b + 5)

d)

4b³(b⁴ + b² + 4b)

17.

Factor
k² - 2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

18.

Factor:
x²+ 7x + 12

a)

(x - 3)(x + 4)

b)

(x + 3)(x - 4)

c)

(x - 3)(x - 4)

d)

(x + 3)(x + 4)

19.

Factor
x² - 9x + 18.

a)

(x - 3)(x - 6)

b)

(x + 6)(x - 3)

c)

(x - 9)(x - 2)

d)

(x - 6)(x + 3)

20.

Factor
x²+ 4x - 32

a)

(x+8)(x-4)

b)

(x-8)(x-4)

c)

(x-8)(x+4)

d)

(x+8)(x+4)

21.

Factor
3x² + 5x - 12.

a)

(x + 3)(3x - 4)

b)

(3x + 4)(x - 3)

c)

(3x + 3)(x - 4)

d)

(3x - 3)(x + 4)

22.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

23.

Factor:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

24.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

25.

Factor 25x² - 81.

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

cannot be factored

26.

factor completely
81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

(9m-1)(9m+1)

27.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

28.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

29.

Factor:
x² - 10x - 24

a)

(x + 12)(x - 2)

b)

(x - 6)(x - 4)

c)

(x - 12)(x + 2)

d)

(x +6)(x - 4)

30.

What are the factors of 3x²-17x+10

a)

(x-5)(3x-2)

b)

(x+5)(3x+2)

c)

(3x-5)(x-2)

d)

(x+5)(3x-2)

31.

What are the factors of x²+3x-40

a)

(x+10)(x-4)

b)

(x+8)(x-5)

c)

(x+20)(x-2)

d)

(x+1)(x-3)

32.

What are the factors of x²-8x-48

a)

(x-12)(x+4)

b)

(x+12)(x-4)

c)

(x+12)(x+4)

d)

(x-12)(x-4)

33.

Find the factors of 5x²+20x+20

a)

5(x+2)(x+2)

b)

5(x-2)(x-2)

c)

5(x+2)(x-2)

d)

(5x+2)(x+2)

34.

Find the factors of 4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

35.

Factor:
3x²-17x+10

a)

(x-5)(3x-2)

b)

(x+5)(3x+2)

c)

(3x-5)(x-2)

d)

(x+5)(3x-2)

36.

Factor:
4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

37.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

38.

Factor 12x - 20

a)

6(2x - 3)

b)

4(3x - 5)

c)

4x(3x - 5)

d)

3(4x + 6)

39.

True or False?
2x + 6 = 2(x + 3)

a)

True

b)

False

40.

Factor:
4x + 30y

a)

2(x + 15y)

b)

4(x + 15y)

c)

2(2x + 15y)

d)

can't be factored

41.

Factor completely:

x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

42.

Factor
x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

43.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

44.

Find the factors of

5m² - 45m + 90

a)

3(m + 1)(m + 8)

b)

5(m - 3)(m - 6)

c)

2(m - 7)(m + 3)

d)

5(m - 5)(m + 3)

45.

10x + 50

a)

10(10x+50)

b)

10(x+50)

c)

10(x+5)

d)

Cannot be factored

46.

-6y + 36

a)

-6 (y -6)

b)

6 (y + 6)

c)

-6 (1)

d)

cannot be factored

47.

9x + 3

a)

9 (x+1)

b)

3( 3x +1)

c)

3(3x + 3)

d)

cannot be factored

48.

Factor by GCF:
17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

not factorable

49.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

50.

Factor:
2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n²)

c)

2n³(10-8n²)

d)

3n(1-4n)

51.

Factor:
2n³+16n+12

a)

2n(n³+24n+6)

b)

2(n³+8n+6)

c)

2n(n³+8n+6)

d)

3(n³+8n+6)

52.

Factor:
10a⁴+16a+10a²

a)

2a(5a³⁺8+5a)

b)

2a⁴(5a+8a²+5a³)

c)

2a⁴(10+16a+40a²)

d)

3a³(5+8a+a²)

53.

39y⁵ + 12y⁴- 3y³

a)

3y(13y⁴ + 4y³ - y²)

b)

3y³(13y² + 4y - 1)

c)

y³(39y² + 12y - 3)

54.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁵)

d)

3x²(80x³-40-60x⁵)

55.

Factor:
10a⁴+16a+10a²

a)

2a(5a³⁺8+5a)

b)

2a⁴(5a+8a²+5a³)

c)

2a⁴(10+16a+40a²)

d)

3a³(5+8a+a²)

56.

Factor:
24c⁵ - 12c³

a)

6(4c⁵ - 2c³)

b)

12c³(2c²)

c)

12c³(2c² - 1)

d)

12c³(2c² - 0)

57.

39y⁵ + 12y⁴- 3y³

a)

3y(13y⁴ + 4y³ - y²)

b)

3y³(13y² + 4y - 1)

c)

y³(39y² + 12y - 3)

58.

Find the factors

16xy - 24y

a)

4y (4x - 6)

b)

8y (2xy - 3y)

c)

8y (2x - 3)

d)

2xy (8 - 12y)

59.

Find the Factors

36a⁵bc - 12c

a)

12c (3a⁵b - 1)

b)

6c (6a⁵b - 2)

c)

12c (3a⁵b - c)

d)

12abc(3a⁴ - 1)

60.

Factor completely

4a³b⁵ - 18a²b³ + 8a³b³

a)

4a²b³ (ab² - 4 + 2a)

b)

2a²b³ (2ab² - 9 + 4a)

c)

2a²b³ (2ab - 9ab + 4)

d)

a²b (4ab - 18a²b³ + 8ab²)

61.

Factor completely

18x³ + 81x - 27

a)

9x (2x² + 9x - 3)

b)

3 (6x³ + 27x - 9)

c)

9 (2x³ + 9x - 3)

d)

9 (2x² + 9x - 3)

62.

Factor completely

45xy + 15x³y + 10y

a)

5y (9xy + 3x²+ 2y)

b)

5xy (9 + 3x²+ 2)

c)

5x (9y + 3xy + 2)

d)

5y (9x + 3x³ + 2)

63.

Factor completely

21x⁷y⁶ + 30x⁵y⁸ - 18x⁵y⁶

a)

3xy (7x⁴y² + 10x²y⁶ - 6x)

b)

3x⁵y⁶ (7y² + 10 x² - 6)

c)

3x⁵y⁶ (7x²+ 10y² - 6)

d)

3x⁷y⁸ (7y² + 10x² - 6x²y²)

64.

Factor Completely

12abc + 18 ab²c - 6b

a)

6b (2abc + 3b - 1)

b)

6b ( 2ac + 3abc - 1)

c)

6b (2ac + 3abc)

d)

6abc (2 + b)

65.

Factor x² – 16.

a)

(x + 2)(x – 8)

b)

(x – 4)(x – 4)

c)

(x + 4)(x + 4)

d)

(x + 4)(x – 4)

66.

Factor completely.

y² - 196

a)

( y - 14 ) ( y - 14 )

b)

( y + 14 ) ( y - 14 )

c)

( y + 13 ) ( y - 13 )

d)

( y - 13 ) ²

67.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

68.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

69.

x² - 9

a)

(x + 3)²

b)

(x + 3) (x - 3)

c)

(x - 3)²

d)

x + 3(x - 3)

70.

4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

71.

We can't factor using difference of two square this

49x² + 4y². Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

72.

Factor $m^2\ -\ 36$

a)

$(m+18)(m-18)$

b)

$(m+6)^2$

c)

$\left(m\ -\ 6\right)^2$

d)

$(m\ +\ 6)\left(m\ -\ 6\right)$

73.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Unfactorable

74.

Factor x² – 16.

a)

(x + 2) (x – 8)

b)

(x – 4) (x – 4)

c)

(x + 4) (x + 4)

d)

(x + 4) (x – 4)

75.

x² - 9

a)

(x + 3) (x - 3)

b)

(x - 3) (x - 3)

c)

(x + 3) (x - 6)

d)

Can't factor using Diff. of Squares

76.

q² - 121

a)

(q + 11) (q - 11)

b)

(q - 11) (q - 11)

c)

(q + 11) (q + 11)

d)

Can't factor using Diff. of Squares

77.

4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

78.

Factor 4x²- 9

a)

(4x + 9) (4x - 9)

b)

(2x + 3) (2x - 3)

c)

2x - 3

d)

(2x + 4.5) (2x - 4.5)

79.

Factor 4m² - 49

a)

(2m + 7) (2m - 7)

b)

(2m - 7) (2m - 7)

c)

(m² + 7) (m² - 7)

d)

Can't factor using Diff. of Squares

80.

Factor 9n² - 1

a)

(3n + 1) (3n - 1)

b)

(3n - 1) (3n - 1)

c)

(n³ + 3) (n³ - 3)

d)

(3n + 1) (3n + 1)

81.

Factor r² - 9t²

a)

(r + 3t) (r - 3t)

b)

(r - 3t) (r - 3t)

c)

(3r + t) (3r - t)

d)

(r + 3t) (r + 3t)

82.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

83.

Complete the formula:

a³+b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

84.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

85.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

86.

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

a)

No

b)

Yes

c)

Yes, getting GCF first

d)

It is a sum of squares

87.

Fully Factor the Following
216x³+125

a)

6(x+5)³

b)

(6x+5)³

c)

(6x+5)(6x²-30x+25)

d)

(6x+5)(36x²-30x+25)

88.

Factor this sum of cubes:

2x³ + 128

a)

2(x³ + 64)

b)

(x + 4)(x² - 4x + 16)

c)

2(x - 4)(x² + 4x + 16)

d)

2(x + 4)(x² - 4x + 16)

89.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Use the X-Puzzle

90.

64-27a³

a)

(4-3a)(9a²+12a+16)

b)

(3a-4)(3a²+12a+16)

c)

(4-3a)(3a²+12a+16)

d)

(4-3a)³

91.

Factor completely $64x^6+y^6$

a)

$\left(4x^2+y^2\right)\left(16x^4-4x^2y^2-y^4\right)$

b)

$\left(4x^2-y^2\right)\left(16x^4+4x^2y^2+y^4\right)$

c)

$\left(4x^2+y^2\right)\left(16x^4-4x^2y^2+y^4\right)$

d)

$\left(4x^2-y^2\right)\left(16x^4-4x^2y^2-y^4\right)$

92.

Which of the following is the complete factored form of $x^3y^9+1000$

a)

$\left(xy^3+10\right)\left(x^2y^6-10xy^3+100\right)$

b)

$\left(xy^{ }+10\right)\left(x^2y^2-10xy^{ }+100\right)$

c)

$\left(xy^3-10\right)\left(x^2y^6+10xy^3+100\right)$

d)

$\left(xy^3-10\right)\left(x^2y^6-20xy^3+100\right)$

93.

125x³ + 8

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(4x + 1)(16x² + 4x + 1)

d)

(4x - 3)(16x² + 12x + 9)

94.

64x³ + 1

a)

(4x - 3)(16x² + 12x + 9)

b)

(3x - 1)(9x² + 3x + 1)

c)

(2x - 1)(4x² + 2x + 1)

d)

(4x + 1)(16x² - 4x + 1)

95.

Level 2 Question 14
8x⁶ - 64

a)

Prime

b)

8(x²- 2)³

c)

8(x²-2)(x⁴+2x²+4)

d)

8(x-2)⁶

96.

What is the factored form of 5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

97.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

98.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

99.

x³-5x²+5x-25

a)

(x²-5)(x-5)

b)

(x²+5)(x-5)

c)

(x²+5)(x+5)

d)

(x²-1)(x-25)

100.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

101.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

102.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

103.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

104.

Factor by grouping:

6x³+3x²+10x+5

a)

(3x²-5)(2x+1)

b)

(3x²+5)(2x+1)

c)

(3x²+5)(2x-1)

d)

(3x²-5)(2x-1)

105.

Solve for x:
6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

106.

2x + 3(5x - 7) = 47

a)

1

b)

2

c)

3

d)

4

107.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

108.

-11 + 3(b + 5) = 7

a)

1

b)

-1

c)

3

d)

-3

109.

7(1 - y) = -3(y - 2)

a)

x = 1/4

b)

x = 4

c)

x = 5

110.

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

111.

Solve the equation, if possible.
$2a-6\left(a-4\right)=\ -4$

a)

7

b)

identity

c)

0

d)

-5

112.

Solve the equation, if possible.
$10z-4=2\left(5z-2\right)$

a)

2

b)

no solution

c)

identity

d)

5

113.

Solve the equation, if possible.
$6m+5-3m=7\left(m-1\right)$

a)

3

b)

no solution

c)

identity

d)

5

114.

Find the error in the problem below
19 - 2k = 3k - 1
+3k +3k
19 + 1k = -1
-19 -19
k = -20

a)

They should have divided by 1 for the last step

b)

They should add 19 instead of subtracting 19

c)

I can not find an error

d)

Instead of adding 3k they should subtract 3k

115.

4 = 2(x + 3)

a)

1/2

b)

7/2

c)

-1

d)

5

116.

Solve: 5x - 14 = 8x + 4

a)

6

b)

-6

c)

-18/13

d)

10/3

117.

3y+6+4y-7=-8

a)

y=-1

b)

y=-8

c)

y=1

d)

y=7

118.

10(h+1)-4=76

a)

h=10

b)

h=4

c)

h=7

d)

h=76

119.

Solve for v.

a)

60

b)

-3

c)

15

d)

3

120.

6(6v +6) - 5 = 1 + 6v

a)

1

b)

-1

c)

no solution

d)

all real numbers

121.

What would be the best first step to solving the equation?
-3=x+5

a)

add 3 to both sides

b)

subtract 5 from both sides

c)

add 5 to both sides

d)

subtract -5 from both sides

122.

4 + k/2 = -3

a)

14

b)

-14

c)

4

d)

-2

123.

3y+4y+6=20

a)

y=2

b)

y=-2

c)

y=4

d)

y=3

124.

Which of the following are basic rules used for solving algebraic equations?

a)

Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

b)

Negative signs can be ignored

c)

Always start on the left side, regardless of where the variable is

d)

Always do the opposite operation

125.

What is the first step to solve this equation: -11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

126.

3x-18=22-2x

a)

x=8

b)

x=2

c)

x=18

d)

x=3

127.

12+5w=15+4w

a)

w=1

b)

w=3

c)

w=5

d)

w=4

128.

0+10x=60-2x

a)

x=60

b)

x=2

c)

x=5

d)

x=10

129.

5h+4=12+h

a)

h=12

b)

h=2

c)

h=0

d)

h=5

130.

23-9x=-56x-28

a)

-1.09

b)

-1

c)

0

d)

2.9

131.

Solve the inequality: 3x + 5 > 2x - 7

a)

x > 10

b)

x = -5

c)

x > -12

d)

x < -12

132.

Solve the inequality: 4(2x - 3) + 5 < 3(4x + 2) - 1

a)

x > 2

b)

x = 2

c)

x > 3

d)

x < 2

133.

Solve the inequality: 2(x + 3) - 4 > 3(x - 2) + 5

a)

x > 10

b)

x < 9

c)

x = 9

d)

x > 9

134.

Solve the inequality: 2(3x - 1) + 4 < 5(2x + 2) - 3

a)

x < 3

b)

x = 3

c)

x > 5

d)

x > 3

135.

Solve the inequality: 2(x - 4) + 3 > 4(x + 1) - 2

a)

x = 5

b)

x < 5

c)

x > 10

d)

x > 5

136.

Solve the inequality: 3(2x + 1) - 5 < 4(3x - 2) + 1

a)

x < 3

b)

x = 3

c)

x > 3

d)

x > 5

137.

Solve the inequality: 5(x - 2) + 3 > 2(x + 4) - 1

a)

x < 5

b)

x > 10

c)

x > 5

d)

x = 5

138.

Solve the inequality: 4(3x - 2) + 5 < 3(4x + 1) - 2

a)

x < 3

b)

x > 3

c)

x = 3

d)

x > 5

139.

Solve the inequality: 2(x + 1) - 3 > 3(x - 2) + 4

a)

x > -5

b)

x > 5

c)

x = -5

d)

x < -5

140.

Solve the inequality: 3(2x - 1) + 4 < 4(3x + 2) - 1

a)

x < 5/2

b)

x > 5/2

c)

x > 2

d)

x = 5/2

141.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

142.

Solve the absolute value equation.

a)

{7}

b)

{-7, 7}

c)

{0, 7}

d)

No Solution

143.

|8 - 4x| = 16

a)

x = -2, x = -6

b)

x = 2 , x = 24

c)

x = -2, x = 6

d)

No Solution

144.

∣2x + 9∣ = 15

a)

x = 3

b)

x = 3

x = -6

c)

x = 3

x = -12

d)

x = 6

x = -12

145.

Solve |2x –3| + 5 =10.

a)

-1, 1

b)

-1, 4

c)

-1, -4

d)

1, 4

146.

|v + 8| − 5 = 2

a)

{-15,-1}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

147.

Solve for x
l 5x l = 40

a)

x = 8 and x =-8

b)

x = 35 and x = -35

c)

Only x = 8

d)

No Solution

148.

Solve for x

l 2x−1 l = 9

a)

x = 5 and x = - 4

b)

x = 5 and x = - 5

c)

Only x = 5

d)

No Solution

149.

Solve for x
l x−6 l + 4= 10

a)

x = 12 and x = 0

b)

x = 3 and x = -3

c)

x = -12 and x = 0

d)

No Solution

150.

Solve for x

2 lx−4l + 8 = 18

a)

x = 9 and x = -1

b)

x = 1 and x = -9

c)

x= 4 and x = -2

d)

No Solution

151.

|−2n| + 10 = −50

a)

{30, -30}

b)

{20, -20}

c)

{-5, 5}

d)

No Solution

152.

Solve |x – 12| - 3 = 11.

a)

-2, -26

b)

-2, 26

c)

3, 25

d)

4, -7

153.

$\left|x\right|=\ -\ 5$

a)

5

b)

-5

c)

5 or -5

d)

no solution

154.

$\left|x\right|\ =\ 6$

a)

6

b)

-6

c)

6 or -6

d)

no solution

155.

What are the steps to solve this: $2\ +\ \left|x-4\right|\ =\ 5$

4 lines

156.

What are the steps to solve this: $3\left|x+1\right|\ +2=4$

4 lines

157.

$\left|x+5\right|\ =\ -3$

a)

$-2\ or\ -8$

b)

no solution

c)

$0$

158.

$\left|x+5\right|=0$

a)

no solution

b)

$0$

c)

$-5$

d)

$-5\ or\ 5$

159.

Solve:
$\left|\frac{3}{4}a-3\right|=9$

a)

$\left\{16,\ -8\right\}$

b)

$\left\{16,\ -16\right\}$

c)

$\left\{-8,\ 8\right\}$

d)

no solution

160.

What could the value of x be?

$|x|=7$

Choose all that apply.

a)

7

b)

-7

c)

14

d)

0

161.

Solve for x

$|x+3|=1$

Don't forget to choose two answers!

a)

-4

b)

4

c)

2

d)

-2

e)

I am not sure.

162.

Solve for x:

$|2x-3|=5$

Choose two answers.

a)

4

b)

-1

c)

1

d)

-4

e)

I am not sure.

163.

Match the following

a)

|x| = 5

1.

x = 5, -5

b)

|2x| = 4

2.

x = 2, -2

c)

|x+2| = 6

3.

x = 4, -8

d)

|x-3| = 2

4.

x = 1, 5

e)

$\left|\frac{x}{5}\right|=-6$

5.

No Solution

164.

What's a way to define absolute value?

a)

The value of a number

b)

The opposite of a number

c)

The distance of a number from zero

d)

The multiplicative inverse of a number

165.

What is the reason that absolute value is always written as a positive?

a)

Absolute value is talking about numbers so it must be positive.

b)

Absolute value does not always have to be positive.

c)

Absolute value is like a clock it has only positive numbers.

d)

Absolute value is talking about distance, distance is always measured by positive numbers.

166.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-3,-1}

c)

{-3}

d)

No Solution

167.

What would be the correct way to write the problem before solving?

2|x-1|-6=4

a)

|x-1|=5

b)

x-1=5

c)

|x-1|=-5

d)

x-1=-5

168.

Solve for X

2|X+3|+3=1

a)

X= -4 and X= -2

b)

X=2 and X= -2

c)

X=0

d)

No Solution

169.

Solve for x
∣ 2x + 9 ∣ = 15

a)

x = 3

b)

x = 3 x = -6

c)

x = 3 x = -12

d)

x = 6 x = -12

170.

Solve for x
| m - 2 | < 8

a)

9 > m > 8

b)

2 < m < -6

c)

-6 < m < 10

d)

0 > m < 0

171.

Solve for x
∣ -2x + 9 ∣ > 15

a)

x<-3 or x>12

b)

-3 < x < 12

c)

x<-3 and x>12

d)

-3 < x > 12

172.

6x + 2 + 6x < 14

a)

x < 1

b)

x > 1

c)

x < -1

d)

x > -1

173.

a)

A

b)

B

c)

C

d)

D

174.

a)

A

b)

B

c)

C

d)

D

175.

a)

v>5 or v<-5

b)

v≥5 or v≤-5

c)

v>-5 or v<5

d)

all real numbers

176.

Describe the first step in solving the absolute value inequality

a)

Add 5 on both sides

b)

Divide both sides by -5

c)

Set up two inequalities

d)

no solution

177.

v>5 or v<-5 v≥5 or v≤-5 v>-5 or v<5 all real numbers

a)

v>5 or v<-5

b)

v≥5 or v≤-5

c)

v>-5 or v<5

d)

all real numbers

178.

a)

n > 1 or n < -7

b)

n > -1 or n < -7

c)

-7 < n < -1

d)

no solution

179.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

180.

28 − k ≥ 7(k − 4)

a)

k ≥ -7

b)

k ≤ -7

c)

k ≥ 7

d)

k ≤ 7

181.

You want to spend at most $1200 on a new laptop. If you make a $400 down payment, then pay the same amount every month for 12 months. Which Inequality could be use to solve to find out how much you can pay each month.

a)

12x + 1200 > 400

b)

12x + 400 < 1200

c)

12x + 400 > 1200

d)

12x + 400 < 1200

182.

Your taxi fare is $2.50 per mile, plus a $5 fee. You cannot exceed $20. Which inequality models this scenario?

a)

5x + 2.50 ≤ 20

b)

2.50x + 5 < 20

c)

2.50x + 5 ≤ 20

d)

7.50x < 20

183.

Solve for x
|−2n| + 10 = −50

a)

{30, -30}

b)

{20,-20}

c)

{-5,5}

d)

No Solution

184.

Solve for x
l 2x−1 l +4 = 8

a)

x = 2.5 and x = -1.5

b)

x = 2 and x = -1

c)

x = -2 and x = 9

d)

No Solution

185.

Solve for x
| 6 - 2x | = -5

a)

11/2, 1/2

b)

-5, 5

c)

1, 3

d)

⊘ No solution

186.

Write an inequality for Graph 4.

a)

-2 < x < 5

b)

x < -2 or x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x ≤ 5

187.

Solve the following equation:

|2x – 3| + 5 = 10.

a)

{−1, 1}

b)

{−1, 4}

c)

{−1, −4}

d)

{1, 4}

188.

When graphing an inequality, you use an open dot when you use which symbol?

a)

<, >

b)

≤, ≥

189.

What inequality is graphed?

a)

x > 2 and x ≤ -3

b)

x > 2 and x < -3

c)

x > 2 or x ≤ -3

d)

x > 2 or x < -3

190.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-2 ≤ x ≤ 6

c)

-3 ≤ x ≤ 3

d)

1 ≤ x ≤ 3

191.

Solve:

3x + 2 < -7 or -4x + 5 < 1

a)

All real numbers

b)

x < -3 and x > 1

c)

x < -3 or x < 1

d)

x < -3 or x > 1

192.

Which of the following would result in NO SOLUTION?

a)

x < 1 or x > 5

b)

x > 1 or x < 5

c)

x < 1 and x > 5

d)

x > 1 and x < 5

193.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

194.

Solve:
3(x - 2) < 2(x + 9)

a)

x<24

b)

x>12

c)

x<12

d)

x>24

195.

You flip an inequality symbol when you...

a)

subtract

b)

multiply and divide only

c)

multiple by a negative number

d)

multiple or divide by a negative number

196.

Your family needs 2 gallons of water this week, but you don’t want to buy any more than 8 gallons. Write an inequality representing the possible gallons of water you could buy this week.

a)

2 ≤ x ≤ 8

b)

2< x < 8

c)

8 ≥ x ≥ 2

d)

2> x > 8

197.

A taxi cab costs $1.75 and $0.75 for each additional mile. You have $20 to spend on you ride. Which inequality could be solved to find how many miles you can travel, if m is the number of additional miles?

a)

1.75n + 0.75 ≥ 20

b)

1.75n + 0.75 ≤ 20

c)

0.75n + 1.75 ≥ 20

d)

0.75n + 1.75 ≤ 20

198.

Solve 24 > -3r > -9

a)

-8 < r < 3

b)

-8 > r > 3

c)

r > - 8 and r > 3

d)

r > -8 or r < 3

199.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

200.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-3,-1}

c)

{-3}

d)

No Solution

201.

$\left|5+10n\right|+4=69$

a)

3 and -7

b)

-7 and -2

c)

12 and -4

d)

6 and -7

202.

$\frac{\left|x+3\right|}{4}=2$

a)

$5\ and\ 11$

b)

$\frac{1}{3}\ and\ -3$

c)

$-\frac{5}{3}\ and\ -5$

d)

$1\ and\ 3$

203.

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

a)

5x + 10 ≥ 100

b)

5x - 100 ≥ 10

c)

10x + 5 ≤ 100

d)

5x + 10 > 100

204.

Solve for x
l 5x l = 40

a)

x = 8 and x =-8

b)

x = 35 and x = -35

c)

Only x = 8

d)

No Solution

205.

Evaluate each expression.
| x + 9 | = -5

a)

-14

b)

-4

c)

{-14, -4}

d)

no solution

206.

What is the reason that absolute value is always written as a positive?

a)

Absolute value is talking about numbers so it must be positive.

b)

Absolute value does not always have to be positive.

c)

Absolute value is like a clock it has only positive numbers.

d)

Absolute value is talking about distance, distance is always measured by positive numbers.

207.

|−2n| + 10 = −50

a)

{30, -30}

b)

{20,-20}

c)

{-5,5}

d)

No Solution

208.

Solve the following equation:

∣ 2x + 9 ∣ = 15

a)

x = 3

b)

x = 3, x = −6

c)

x = 3, x = −12

d)

x = 6, x = −12

EXTRA PRACTICE: Units 1 and 2

Total questions: 208

Worksheet time: 16hrs 36mins

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