Free Printable Algebra 1: Topic 1 (Solving Equations & Inequalities)

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Algebra 1: Topic 1 (Solving Equations & Inequalities)

Total questions: 60

Worksheet time: 2hrs 4mins

Name

Class

Date

s - 10 ≤ 1

s ≤ 11

s ≤ 9

s ≥ 11

s ≥ 9

What inequality does the number line graph represent?

$x\le-4$

$x\ge-4$

x < -4

x < 4

What inequality does the number line graph represent?

$x\ge3$

x > 3

x < -3

$x\le3$

When you graph an inequality, you used a closed dot when you use which symbols?

≤, ≥

<, >

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

<, >

≤, ≥

Solve the inequality.

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

b > 20

b > 6

b > 14

b > 20

Solve the inequality.

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

$d\ \le3$

$d\ \le-3$

$d\ \ge\ 3$

$d\ \ge\ -3$

You flip an inequality symbol when you...

subtract

multiply and divide only

multiple by a negative number

multiple or divide by a negative number

Which of the following situations shows the need to flip the inequality sign?

$3x<-9$

$\frac{x}{-4}>8$

$x-2\le-4$

$x--1\ge6$

10.

The steps in solving 5b - 6 = 24 are:

Add 6 to both sides and divide both sides by 5

Add 6 to both sides and multiply both sides by 5

Subtract 6 from both sides then multiply both sides by 5

Subtract 6 from both sides then divide both sides by 5

11.

$3+\frac{1}{4}a=31$

a= 28

a= 112

a= 7

a= 67

12.

-42

-24

13.

22.95 = 16.15 + 4x

x = 9.775

x = 4.2

x = 1.7

x = 2.2

14.

Which of the following represents the solution to the inequality shown below?

-6x - 8 > -32

x < 4

x > 4

x < $6\frac{2}{3}$

x > $6\frac{2}{3}$

15.

Justin and Sean have a classics album collection.

 The number of albums in Justin’s collection can be represented by x.

 The number of albums in Sean’s collection is 5 times the number in Justin’s collection.

 The total number of albums in both collections is 78.

What is x, the number of albums in Justin’s collection?

x = 6

x = 15.6

x = 13

x = 78

16.

Grace, Maci, and Kendra all have a large collection of earrings.

 The number of pairs of earrings in Grace’s collection is represented by x.

 The number of pairs of earrings in Maci’s collection is three times the number of pairs in Grace’s collection.

 Kendra has 4 earrings in her collection.

 The total number of pairs of earrings in all three girls’ collections is 52.

How many pairs of earrings are in Maci’s collection?

x = 48

x = 12

x = 36

x = 4

17.

Solve: 3(x-2)=18

6.7

-4

18.

2x-3+4x=27

19.

$2x=\frac{5x-12}{3}$

What is the second step when solving this?

Multiply by 3

Divide by 5

Add 12

Subtract 5x

20.

Solve for the variable k in the following equation:

7k − 1 − 6k = −6

k=-2

k=-3

k=-4

k=-5

21.

Solve for the variable h in the following equation:

10( h + 1) - 4 = 76

h=10

h=4

h=7

h=76

22.

Rachel states that -5.5 is an integer because it is negative.

Is she correct?

Why or why not?

Yes, because all negatives are integers.

Yes, because all integers have decimals.

No, because integers do not have decimals.

No, because integers cannot be negative.

23.

Classify this number: 6.7

real

real rational

real rational integer

real rational integer whole

24.

Is ½ a terminating decimal or a repeating decimal?

terminating decimal

repeating decimal

25.

-4 is not a whole number because:

It's negative and whole numbers are positive.

it's irrational.

it cannot be turned into a fraction.

it is even.

26.

Solve for x
l 4x−3 l = 17

x = 5 and x =-3.5

x = 0 and x = -5

x = 10 and x = -10

No Solution

27.

Solve for x
l x−6 l + 4= 10

x = 12 and x = 0

x = 3 and x = -3

x = -12 and x = 0

No Solution

28.

−2|−2r − 4| = -12

{3,1}

{-5,1}

{-3}

No Solution

29.

Solve the following equation:

|−2n| + 10 = −50

{30, −30}

{20, −20}

{−5, 5}

No Solution

30.

Solve: |x + 3| < 8

x > 5 or x < -11

-11 < x < 5

x > 11 or x < -5

5 < x < 11

31.

Solve:
|x + 3| > 8

x > 5 or x < -11

-11 < x < 5

x > 11 or x < -5

-5 < x < 11

32.

Solve: |x - 3| < 8

x > 5 or x < -11

-11 < x < 5

x > 11 or x < -5

-5 < x < 11

33.

Solve: |2x + 1| ≤ 19

x ≥ 9 or x ≤ -10

-10 ≤ x ≤ 9

x ≥ 10 or x ≤ -9

-9 ≤ x ≤ 10

34.

A fitness club opens with 80 members. Each month the membership increases by 15 members. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

y=15x

y=15x+80

y=x+15

y=80x+15

35.

Which of the following situations could be descried by the equation y= -25x + 120

There are 120 people in the football stadium, and 25 more are entering each hour.

A plumber charges $25 for a house call and $120 per hour.

A teacher has 120 students. Her third period has 25 students

There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

36.

Which of the following situations could be descried by the equation y= -25x + 120

There are 120 people in the football stadium, and 25 more are entering each hour.

A plumber charges $25 for a house call and $120 per hour.

A teacher has 120 students. Her third period has 25 students

There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

37.

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation for C, the total cost, to rent the boat for h hours.

h = 2C + 15

C = 15h + 2

h = 15C + 2

C = 2h + 15

38.

Which equation would describe "two times a number plus five equals 15"?

x + 5 = 15

2x + 5=15

x + 2(5) = 15

2(x + 5) = 15

39.

A plumber charges $50 to make a house call. He also charges $25 per hour for labor.

How much would it cost for 2.5 hours of labor?

$100

4.50

$112.50

$65.00

$123.45

40.

You are visiting Baltimore, MD and a taxi company charges you a flat fee of $3.00 for using the taxi and $0.75 per mile.

Which of the following equations matches the situation?

0.75x + 3y = 50

y = 0.75x + 3

y = 3x + 0.75

3x + 0.75y = 50

50 = -0.75x + y

41.

For a field trip, 21 students rode in cars and the rest filled six buses. How many students were in each bus if 189 students were on the trip?

31.5 students per bus

28 students per bus

27 students per bus

24 students per bus

42.

A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.

c = 2.75b + 4

c = 2.75b

c = 4b- 2.75

c = 2.75b - 4

43.

A movie ticket costs $12. If you buy m tickets, write an equation to find the total amount spent on tickets.

total_cost = m / 12

total_cost = 12 + m

total_cost = 12 * m

total_cost = 12 - m

44.

What mistake did Student A make?

Step 1: Distributed Incorrectly

Step 2: Combined Like Terms Incorrectly

Step 3: Combined Like Terms Incorrectly

Step 4: Didn't Flip the Inequality

45.

What mistake did Student B make?

Step 1: Distributed Incorrectly

Step 2: Combined Like Terms Incorrectly

Step 3: Combined Like Terms Incorrectly

Step 4: Didn't Flip the Inequality

46.

x < 1

x < -1

x > 1

x > -1

47.

n < 1

n < -1

n > 1

n > -1

48.

WRITE AN EQUATION
Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

24-10=7x

24-7x=10

10+7x=24

10+x=14

49.

Where did Rajendra make an error in his calculation?

Step 1

Step 2

Step 3

Rajendra is correct.

50.

Ainsley bought some shirts for her clothing store $15 each. She received $50 off her entire purchase and spent a total oof $400. Which equation shows how many shirts Ainsley purchased for her store?

15x + 50 = 400

15 - 50x = 400

15x - 50 = 400

50 - 15x = 400

51.

Shaan bought a video game console and some games for $350. The video game console cost $200. Each game cost $25. Write an equation that represents how many games Shaan purchased.

350 + 25x = 200

200 + 25x = 350

200 + 25x > 350

200x + 25 = 350

52.

Karis has $900 in the bank. Every time she rides the bus she spends $2. Write an inequality that Karis can use to see how many time she can ride the bus and still have more than $500 in the bank.

900 + 2x < 500

900 + 2x > 500

900 - 2x > 500

900 - 2x < 900

53.

There are 125 members in the school marching band. The band wants to raise at least $25,000 for a trip to a national competition. The school agreed to contribute $5,000 towards the trip. Which inequality shows the amount of money that each band member should raise?

125x + 25,000 ≥ 5,000

125x + 5,000 ≥ 25,000

5,000x + 125 ≥ 25,000

5,000x + 25,000 ≥ 125

54.

Which equation has x=9 as a solution

4 + x = 12

5x = 45

2x = 20

x + 7 = 26

55.

Sandy is upgrading her internet service. Comcast charges $60 for installation and $50.45 per month of service. AT&T has free installation but charges $57.95 per month. How many months would I have to have cable for to pay the same amount with both companies? Identify the equation that models this situation.

60x + 50.45 = 57.95

60x + 50.45 = 57.95x

60 + 50.45x = 57.95x

60x + 50.45x = 57.95x

56.

A twelve inch candle and an 18 inch candle are lit at 6pm. The 12 inch candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Identify the equation that models this situation.

12 - 0.5x = 18 - 2x

12 + 0.5x = 18 + 2x

12x - 0.5 = 18x - 2

12 - 6x = 18 - 2x

57.

-3 < x + 6 ≤ 5

-9< x or x≤ -1

All Real numbers

-9< x and x≤ -1

-10< x and x≤ -7

58.

The school cafeteria seats 250 students. 203 students are already seated. Write and solve an inequality that represents the additional number of students that can be seated.

203 + s ≤ 250; 47 students

250 - 203 = x; 47 students

203 + s < 250; 47 students

x + 203 = 250; 47 students

59.

Your class needs to raise $1000 for a field trip. You have already raised $250. You all decide to sell coupon books. You earn $12.50 for each book sold.
Choose the inequality that represents the number of books you should sell to meet or exceed your goal.

b(250 + 12.50) ≥ 1000

250 + 12.50b ≥ 1000

250 + 12.50 + b ≥ 1000

b ≥ 1000 - 250 - 12.50

60.

Find the Error
What error did the student make when solving the equation:
⅕x + 6 = ⅗x + 5
1x + 6 = 3x + 5
-2x + 6 = 5
-2x = -1
x = 1/2

The student found an incorrect common denominator

The student did not multiply all terms by the common denominator

The student did not use opposite operations appropriately

The student did not correctly eliminate the variable from one side of the equation

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Algebra 1: Topic 1 (Solving Equations & Inequalities)

Total questions: 60

Worksheet time: 2hrs 4mins

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