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
- $45,000
- $48,000
- $50,000
- $52,500
- $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.
x
3
=
2x + 3
7
- −3
- 2
- 3
- 37
- 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(2y + 4) = 8y
- −8
- −6
- −2
- 2
- 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
|x + 5| = 3
- −8
- −3
- −2
- −8 and −3
- −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.
- 28
- 35
- 38
- 58
- 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
- −3
- −13
- 13
- 3
- 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
- 3 < x < 11
- 9 < x < 11
- 9 < x < 121
- x < 3 or x < 11
- 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
- 24 years old
- 27 years old
- 30 years old
- 36 years old
- 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 miles
- 13 miles
- 14 miles
- 26 miles
- 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.
13 − 2(2x + 1) = 1
- −72
- −52
- 94
- 52
- 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.