Free Printable Solving Inequalities: Variety

1.

3x - 2 < 13

a)

x > 3.67

b)

x > 5

c)

x < 5

d)

x < 3.67

2.

.5(x - 8) < 2

a)

x > 20

b)

x < 20

c)

x > 12

d)

x < 12

3.

3(x - 3) ≤ 2(x + 2)

a)

x ≤ -5

b)

x ≥ 5

c)

x ≥ 13

d)

x ≤ 13

4.

Solve the inequality.

30 + n ≥ 50

a)

n > 50

b)

n ≥ 80

c)

n < 30

d)

n ≥ 20

5.

-4 + y < -8

a)

y < 4

b)

y < -12

c)

y < -4

d)

y < 12

6.

-8x < 48

a)

x < -6

b)

x > -6

c)

x < 6

d)

x > 6

7.

Solve:

a)

x < 24

b)

x < 3

c)

x > 24

d)

x < 10.3333....

8.

10 ≥ x - 3

a)

x ≤ 13

b)

x ≥ 13

c)

x ≤ 7

d)

x ≥ 7

9.

hint: need to get rid of the 3 first

a)

x ≥ 11

b)

x ≤ 19

c)

x < 11

d)

x > 19

10.

a)

x > 3

b)

x ≤ ⅕

c)

x ≥ 3

d)

x ≤ ⅕

11.

a)

x < 6

b)

x ≤ 6

c)

x < 5.5

d)

x < 3/2

12.

hint: move 11 first

a)

x ≤ 12

b)

x ≥ 12

c)

x ≥ 14

d)

x ≥ 23

13.

Solve

-2(x + 2) < 14

a)

x < - 5

b)

x > -5

c)

x < -9

d)

x > -9

14.

6(n + 2) < -72

a)

n < -14

b)

n < 35/3

c)

n < -10

d)

∞

15.

Solve the inequality.
-8k - 4 ≤ -60

a)

k < 7

b)

k > 7

c)

k ≤ 7

d)

k ≥ 7

16.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

17.

-2x + 3(-4x + 6) ≤116

a)

x ≤ -7

b)

x ≥ 29

c)

x ≥ -7

d)

x ≤ 29

18.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

19.

$4\left(y+4\right)\le16$

a)

$y\le0$

b)

No Solution

c)

$y\le2$

20.

5z - 2z - 2 < 13

a)

z > 5

b)

z < 5

c)

z > 1

d)

z < 1

21.

-7 + 10z > -27

a)

z < -2

b)

z > -34

c)

2 > z

d)

z > -2

22.

10 < 3x + 19

a)

x < 3

b)

x > 3

c)

x < -3

d)

x > -3

23.

-8x < 48

a)

x < -6

b)

x > -6

c)

x < 6

d)

x > 6

24.

11x + 16 < 43 + 2x

a)

x ≥ 5

b)

x < 3

c)

x > 5

d)

x ≤ 3

25.

4 - 7y ≤ 18

a)

y ≤ -2

b)

y ≤ -8

c)

y ≤ 3.1415926589

d)

y ≥-2

26.

14 + 9x > 6x + 4

a)

x > 12

b)

x > -3 1/3

c)

x > 3

d)

x ≥ 6

27.

Does the given value make the inequality true? x + 9 > 21, when x = 15

a)

True

b)

Not True

28.

Solve:
-4(-7-5x) > 188

a)

x < -32

b)

x > -32

c)

x < 8

d)

x > 8

29.

-138 ≥ -6(6b − 7)

a)

b ≤ 5

b)

b ≤ -5

c)

b ≥ 5

d)

b ≥ -5

30.

3(d + 2) < -15

a)

d < -7

b)

d > -7

c)

d < -11

d)

d > 1

31.

-2 (x+2) < 14

a)

x < - 5

b)

x > -5

c)

x < -9

d)

x > -9

32.

−9e − 8 + 4e ≤ −1

a)

−35 ≥ e

b)

−1⅖ ≥ e

c)

−1⅖ ≤ e

d)

8⅕ ≤ e

33.

What is the inequality sign for greater than?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

34.

If you divide an inequality with a less than sign by -3, what inequality sign would it change to?

a)

$>$

b)

$<$

c)

$\ge$

d)

$\le$

35.

When looking at this inequality what should be your first step? $-1-6x-6>-11-7x$

a)

Get rid of parentheses

b)

move x terms to the LHS

c)

combine like terms

d)

move the constant to the RHS

36.

You try!

Solve.
$1-3x\ +6x>10-6x$

a)

x > 1

b)

x < -1

c)

x > 9

d)

x < 9

37.

Would the inequality sign flip? (Type Yes or No)

$-2x\ +3<\ 8$

(a)

38.

When looking at this inequality what should be your first step? $3(1-2x)>3-6x$

a)

Get rid of parentheses

b)

move x terms to the LHS

c)

combine like terms

d)

move the constant to the RHS

39.

How comfortable are you with solving inequalities?

a)

Great!

b)

So-so

c)

Totally Confused

40.

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

a)

x<24

b)

x>12

c)

x<12

d)

x>24

41.

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

42.

Solve the inequality: 3x + 5 > 10

a)

x > 10

b)

x = 5/3

c)

x > 5/3

d)

x < 5/3

43.

Solve the inequality: 2x - 7 < 15

a)

x > 11

b)

x < 4

c)

x < 11

d)

x > 15

44.

Solve the inequality: 4(x - 3) ≥ 20

a)

x ≤ 8

b)

x > 8

c)

x ≤ 3

d)

x ≥ 8

45.

Solve the inequality: 2(x + 5) < 8

a)

x < 1

b)

x > 1

c)

x < -1

d)

x > -1

46.

Solve the inequality: 3 - 2x > 7

a)

x > -2

b)

x < 2

c)

x < -2

d)

x > 5

47.

Solve the inequality: 5x + 2 ≤ 12

a)

x ≤ 2

b)

x = 2

c)

x > 2

d)

x ≥ 2

48.

Solve the inequality: 2(x - 4) > 10

a)

x > 9

b)

x > 11

c)

x > 5

d)

x > 7

49.

Solve the inequality: 3x + 8 < 5

a)

x < 1

b)

x = -1

c)

x < -1

d)

x > -1

50.

Solve the inequality: 4 - 3x ≥ 10

a)

x ≥ 4

b)

x ≤ 2

c)

x ≤ -2

d)

x ≥ -2

51.

Solve the inequality: 2(x + 3) ≤ 6

a)

x ≥ 0

b)

x > 0

c)

x = 0

d)

x ≤ 0

52.

a)

a ≥ 4

b)

a ≥ -4

c)

a ≤ 4

d)

a ≤ -4

e)

no solution

53.

Solve the inequality.

$2\left(b\ -\ 8\right)\ >\ 12$

a)

b > 20

b)

b > 6

c)

b > 14

d)

b > 20

54.

Solve the inequality.

$-4d\ -\ 9\ \le\ 3$

a)

$d\ \le3$

b)

$d\ \le-3$

c)

$d\ \ge\ 3$

d)

$d\ \ge\ -3$

55.

Solve:
7(x + 3) < 5x + 13

a)

x>-4

b)

x < 17

c)

x<-4

d)

x > -17

56.

54x + 64 ≥ 49x + 59

a)

x≥−1

b)

x≤-1

c)

x>9

d)

x<-3

57.

Solve:
287 ≤ 7(1 + 5p)

a)

p ≤ 8

b)

p ≥ 8

c)

p ≤ 56

d)

p ≥ 56

58.

Do I need to flip my sign when I solve this inequality?
3x ≥ 12

a)

Yes

b)

No

59.

Solve:
8 - 3k < 8(1 - 7k)

a)

k < 5

b)

k > 5

c)

k < -33

d)

k < 0

60.

Solve:
-4(-7-5x) > 188

a)

x < -32

b)

x > -32

c)

x < 8

d)

x > 8

61.

Solve for r

a)

r ≥ 6

b)

r ≥ 10.9

c)

r ≥ 30

d)

r ≥ 75

62.

Solve:

a)

p ≤ -12

b)

p ≥ -12

c)

20 ≥ p

d)

20 ≤ p

63.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

64.

Which is a solution of
5(v + 3) - 10v > -10

a)

v < 5

b)

V > 5

c)

V > -5

d)

v < -5

65.

Which is the solution of
-4 - 6m > -9m + 8?

a)

m < -4

b)

m > 4

c)

m < 15

d)

m > 36

66.

$4\left(2x-1\right)>-7+2x$

a)

$x<-2$

b)

$x<-\frac{1}{2}$

c)

$x>-2$

d)

$x>-\frac{1}{2}$

67.

$2\left(2x+13\right)\ge4\left(-6+x\right)$

a)

$x\ge-6.25$

b)

All Real Numbers

c)

No Solution

d)

$x\le0$

68.

$2h+11>-7+4h-16$

a)

$h<17$

b)

$h<6$

c)

$h>-17$

d)

$h>-6$

69.

What is the FIRST step to solving this inequality?

$-4\left(x-9\right)+2x\ge-27$

a)

Subtract 2x on both sides

b)

Distribute: multiply -4 by x and by -9

c)

Add x to 2x

d)

Add 9 to both sides

70.

x+5x+6>0

a)

x<-6

b)

x<1

c)

x>-1

d)

x<6

71.

3(6x + 2) +3x< 27

a)

$x<-1$

b)

$x<1$

c)

x < 21

d)

x > -21

72.

20x+16-4x\le32

a)

$x\le16$

b)

$x\le-16$

c)

$x\le1$

d)

$x\le1$

73.

12+9𝑗+𝑗\le72

a)

$j\le6$

b)

$j\le-6$

c)

$j<6$

d)

$j<-6$

74.

$3𝑧−15𝑧−30>54$

a)

$z<7$

b)

$z<-7$

c)

$z>-7$

d)

$z>7$

75.

$−5(2𝑥+2)+5x>15$

a)

$x<-5$

b)

$x<5$

c)

$x>5$

d)

$x>-5$

76.

$3(𝑥−2)+5x>18$

a)

$x>-3$

b)

$x<-3$

c)

$x>3$

d)

$x<3$

77.

$18+7𝑛+3+6𝑛≤86$

a)

$n\le-5$

b)

$n\le5$

c)

$5\ge-5$

d)

$n\ge5$

78.

$3𝑥−6≤42-5x$

a)

$x\le6$

b)

$x\le-6$

c)

$x\ge6$

d)

$x\ge-6$

79.

$−6+12y>-16+2y$

a)

$y>1$

b)

$y>-1$

c)

$y<-1$

d)

$y<1$

80.

$6x+2<10+4x$

a)

$x<4$

b)

$x<8$

c)

$x>4$

d)

$x>8$

81.

$-2n-3<2n+9$

a)

$n<-3$

b)

$n<3$

c)

$n>-3$

d)

$n>3$

82.

$4\left(2x-1\right)>-7+2x$

a)

$x<-2$

b)

$x<-\frac{1}{2}$

c)

$x>-2$

d)

$x>-\frac{1}{2}$

83.

3x - 6 < 2(x + 9)

a)

x<24

b)

x>12

c)

x<12

d)

x>24

84.

7(x + 3) < 5x + 13

a)

x>-4

b)

x < 17

c)

x<-4

d)

x > -17

85.

-6x +1 < -35-4x

a)

x < 17

b)

x < 18

c)

x > 18

d)

x > 17

86.

$6+\frac{1}{2}𝑥-4≤10$

a)

$x≤16$

b)

$x≤-16$

c)

$x\ge16$

d)

$x\ge-16$

87.

$6+\frac{1}{3}𝑥-3≤6$

a)

$x≤-9$

b)

$x≤9$

c)

$x\ge9$

d)

$x\ge-9$

88.

$2x-\frac{3}{2}x+2\ge12$

a)

$x\ge5$

b)

$x\le5$

c)

$x\ge20$

d)

$x\le20$

89.

$10+\frac{1}{6}x-15\ge1$

a)

$x\le-36$

b)

$x\le36$

c)

$x\ge-36$

d)

$x\ge36$

90.

$10+\frac{3}{4}x-5>11$

a)

$x>8$

b)

$x>-8$

c)

$x>-1$

d)

$x<4$

91.

$20-\frac{1}{3}x-16>11$

a)

$x<-21$

b)

$x>21$

c)

$x<2.33$

d)

$x<6.67$

92.

$1+p\ge\frac{12}{7}$

a)

$p\ge\frac{5}{7}$

b)

$p\ge\frac{19}{7}$

c)

$p\ge-\frac{5}{7}$

d)

$p\ge\frac{12}{7}$

93.

$1+\frac{1}{10}k<11$

a)

$k<10$

b)

$k>100$

c)

$k<100$

d)

$k>10$

94.

a)

p ≤ -9

b)

p ≥ 9

c)

p ≤ 12

d)

p ≥ -12

95.

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

a)

x<24

b)

x>12

c)

x<12

d)

x>24

96.

$4\left(2x-1\right)>-7+2x$

a)

$x<-2$

b)

$x<-\frac{1}{2}$

c)

$x>-2$

d)

$x>-\frac{1}{2}$

Solving Inequalities: Variety

Total questions: 96

Worksheet time: 24hrs 0mins

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