Free Algebra 1 Practice Test Questions

Use these Algebra 1 practice questions to review basic equation solving, proportions, absolute value, square roots, inequalities, word problems, and algebraic expressions. After answering each question, open the explanation to see how the problem is solved step by step.

Algebra 1 Topics Covered

  • Solving linear equations
  • Working with proportions
  • Using absolute value equations
  • Solving word problems
  • Understanding square roots and inequalities
  • Evaluating algebraic expressions
  • Setting up systems of equations

Algebra 1 Practice Questions

1. This year, a salesman sells a total of $60,000 worth of steak knives by going door-to-door. This represents a 20% increase from the year before. What was the value of his sales last year?

  1. $45,000
  2. $48,000
  3. $50,000
  4. $52,500
  5. $56,000
Show Answer

Answer: C. $50,000

Let x represent the total value of last year’s sales. Since this year’s sales increased by 20%, the current sales are 120% of x, or 1.2x.

1.2x = 60,000

Divide both sides by 1.2:

x = 50,000

Therefore, the salesman sold $50,000 worth of steak knives last year.

2. Solve the equation for x.



x
3

=

2x + 3
7

  1. −3
  2. 2
  3. 3
  4. 37
  5. 9
Show Answer

Answer: E. 9

This equation is a proportion, so it can be solved by cross-multiplication.



x
3

=

2x + 3
7

7x = 3(2x + 3)

7x = 6x + 9

x = 9

3. Solve the equation for y.

3(2y + 4) = 8y

  1. −8
  2. −6
  3. −2
  4. 2
  5. 6
Show Answer

Answer: E. 6

Distribute the 3 first:

3(2y + 4) = 8y

6y + 12 = 8y

Subtract 6y from both sides:

12 = 2y

Divide both sides by 2:

y = 6

4. Solve the equation for x.

|x + 5| = 3

  1. −8
  2. −3
  3. −2
  4. −8 and −3
  5. −8 and −2
Show Answer

Answer: E. −8 and −2

The absolute value of a number is its distance from zero. Since |x + 5| = 3, the expression inside the absolute value can equal either −3 or 3.

x + 5 = −3

x = −8

x + 5 = 3

x = −2

So the solutions are −8 and −2.

5. If 3x + 8x + 4x = 6x + 63, then what is 5x + 23?

  1. 28
  2. 35
  3. 38
  4. 58
  5. 62
Show Answer

Answer: D. 58

First, solve the given equation for x.

3x + 8x + 4x = 6x + 63

15x = 6x + 63

9x = 63

x = 7

Now substitute 7 for x in 5x + 23.

5(7) + 23 = 35 + 23 = 58

6. What is the reciprocal of −3?

  1. −3
  2. 13
  3. 13
  4. 3
  5. Undefined
Show Answer

Answer: B. 13

The reciprocal of a number is the value that multiplies with it to make 1. Since −3 can be written as
31,
its reciprocal is
13.

−3 × 13 = 1

7. If the positive square root of x is between 3 and 11, then what inequality represents all possible values of x?

  1. 3 < x < 11
  2. 9 < x < 11
  3. 9 < x < 121
  4. x < 3 or x < 11
  5. x < 9 or x < 121
Show Answer

Answer: C. 9 < x < 121

If the positive square root of x is between 3 and 11, then:

3 < √x < 11

Square each part of the inequality:

9 < x < 121

8. Carol is three times older than Andrew. Brad is two years older than Andrew. In six years, the sum of Andrew’s and Brad’s ages will be the same as Carol’s age. How old is Carol?

  1. 24 years old
  2. 27 years old
  3. 30 years old
  4. 36 years old
  5. 42 years old
Show Answer

Answer: A. 24 years old

Let A represent Andrew’s current age, B represent Brad’s current age, and C represent Carol’s current age.

C = 3A

B = A + 2

In six years, Andrew’s age plus Brad’s age will equal Carol’s age:

(A + 6) + (B + 6) = C + 6

Substitute A + 2 for B and 3A for C:

(A + 6) + [(A + 2) + 6] = 3A + 6

2A + 14 = 3A + 6

A = 8

Andrew is 8 years old. Carol is three times Andrew’s age:

3 × 8 = 24

So Carol is 24 years old.

9. A cab ride costs $3.25 for the first half-mile and $0.70 for each mile after the first half-mile. How far can someone travel for $12?

  1. 9 miles
  2. 13 miles
  3. 14 miles
  4. 26 miles
  5. 27 miles
Show Answer

Answer: B. 13 miles

Let C represent the total cost and D represent the distance in miles.

The cost is $3.25 for the first half-mile, plus $0.70 for each mile after the first half-mile:

C = 3.25 + 0.70(D − 0.5)

Substitute 12 for C:

12 = 3.25 + 0.70(D − 0.5)

12 = 3.25 + 0.7D − 0.35

12 = 2.9 + 0.7D

9.1 = 0.7D

D = 13

Someone can travel 13 miles for $12.

10. Solve the equation for x.

13 − 2(2x + 1) = 1

  1. 72
  2. 52
  3. 94
  4. 52
  5. 72
Show Answer

Answer: D. 52

First, simplify the left side of the equation.

13 − 2(2x + 1) = 1

13 − 4x − 2 = 1

11 − 4x = 1

Subtract 11 from both sides:

−4x = −10

Divide both sides by −4:

x =
104
=
52

How to Use These Algebra 1 Practice Questions

Start by answering each question without looking at the explanation. Then open the answer and compare your work to the step-by-step solution. If you miss a question, review the topic and try a similar problem before moving on.

For extra review, focus on the question types you missed most often. Algebra 1 skills build on each other, so strengthening basic equation solving, proportions, inequalities, and word-problem setup can make later topics easier.

 

Last Updated: July 3, 2026