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Elementary Algebra Practice Questions

ACT · ACT Math · 135 free MCQs with instant results and detailed explanations.

135
Total
45
Easy
61
Medium
29
Hard

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Sample Questions from Elementary Algebra

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the value of x in the equation 2x + 5 = 13?
A. 4
B. 5
C. 6
D. 8
Show Answer & Explanation
Correct Answer: A
To find x, we first subtract 5 from both sides, giving us 2x = 8. Dividing both sides by 2 results in x = 4.
Q2
Easy
If the expression 3(a + 4) = 21, what is the value of a?
A. 1
B. 3
C. 5
D. 7
Show Answer & Explanation
Correct Answer: B
First, divide both sides by 3 to get a + 4 = 7. Then, subtract 4 from both sides to find a = 3.
Q3
Easy
What is the solution for the equation x^2 - 9 = 0?
A. 3
B. -3
C. Both 3 and -3
D. None of the above
Show Answer & Explanation
Correct Answer: C
Factoring the equation gives (x + 3)(x - 3) = 0. Setting each factor to zero results in x = 3 and x = -3.
Q4
Medium
If 3x + 7 = 22, what is the value of x?
A. 5
B. 6
C. 7
D. 8
Show Answer & Explanation
Correct Answer: A
To find x, first subtract 7 from both sides of the equation: 3x = 22 - 7, which simplifies to 3x = 15. Then, divide both sides by 3, leading to x = 5.
Q5
Medium
If 5y - 2 = 3y + 10, what is the value of y?
A. 6
B. 8
C. 10
D. 12
Show Answer & Explanation
Correct Answer: A
To find y, first subtract 3y from both sides: 5y - 3y - 2 = 10. This simplifies to 2y - 2 = 10. Then, add 2 to both sides and divide by 2, resulting in y = 6.
Q6
Medium
If 3x + 5 = 20, what is the value of x?
A. 5
B. 10
C. 3
D. 15
Show Answer & Explanation
Correct Answer: A
To find x, first subtract 5 from both sides (3x = 15). Then, divide by 3 (x = 5).
Q7
Medium
The product of two consecutive integers is 72. What are the integers?
A. 8 and 9
B. 6 and 7
C. 5 and 6
D. 7 and 8
Show Answer & Explanation
Correct Answer: B
The consecutive integers can be represented as n and n+1. The equation n(n+1) = 72 gives n = 6.
Q8
Hard
If 3x + 2y = 12 and 4x - y = 5, what is the value of x?
A. 2
B. 3
C. 4
D. 5
Show Answer & Explanation
Correct Answer: A
To find the value of x, we can solve the system of equations. From the first equation, we can express y in terms of x: 2y = 12 - 3x, so y = 6 - (3/2)x. Substituting this into the second equation gives 4x - (6 - (3/2)x) = 5. Simplifying this leads to 4x + (3/2)x - 6 = 5, which can be solved to find x = 2.
Q9
Hard
The product of two consecutive positive integers is 342. What are the integers?
A. 18 and 19
B. 20 and 21
C. 17 and 18
D. 16 and 17
Show Answer & Explanation
Correct Answer: A
Let the two consecutive integers be n and n+1. The equation n(n+1) = 342 leads to n^2 + n - 342 = 0. Solving this quadratic equation using the quadratic formula, n = (-1 ± √(1 + 4*342))/2, gives n = 18 (the positive root). Thus, the integers are 18 and 19.
Q10
Hard
If x + 2y = 12 and 3x - y = 9, what is the value of x?
A. 6
B. 4
C. 8
D. 2
Show Answer & Explanation
Correct Answer: A
By solving the equations simultaneously, we find that x = 6. Substituting y from the first equation into the second confirms this.

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Elementary Algebra — ACT ACT Math Practice Questions Online

This page contains 135 practice MCQs for the chapter Elementary Algebra in ACT ACT Math. The questions are organized by difficulty — 45 easy, 61 medium, 29 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.