SOL Algebra I Practice — Questions and Answers
Question 1: Solve for x: 3x + 7 = 22
- x = 5 (Correct answer)
- x = 3
- x = 7
- x = 15
Correct answer: x = 5
Subtract 7 from both sides to get 3x = 15, then divide by 3 to get x = 5.
Start with 3x + 7 = 22. Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Checking: 3(5) + 7 = 15 + 7 = 22, which matches the original equation.
Question 2: What is the slope of the line represented by the equation y = 4x - 9?
- -9
- 4 (Correct answer)
- 9
- -4
Correct answer: 4
In slope-intercept form y = mx + b, m is the slope, so the slope here is 4.
The equation y = 4x - 9 is already in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Here m = 4 and b = -9, so the slope of the line is 4.
Question 3: Simplify the expression: 5(2x - 3) + 4x
- 14x - 15 (Correct answer)
- 10x - 3
- 14x - 3
- 9x - 15
Correct answer: 14x - 15
Distribute 5 to get 10x - 15, then combine with 4x to get 14x - 15.
Distribute the 5 across (2x - 3): 5(2x) - 5(3) = 10x - 15. Then add the remaining 4x: 10x + 4x - 15 = 14x - 15.
Question 4: Which of the following is a factor of x^2 - 9?
- x + 9
- x - 3 (Correct answer)
- x + 4
- x - 9
Correct answer: x - 3
x^2 - 9 is a difference of squares, factoring to (x - 3)(x + 3).
x^2 - 9 fits the pattern a^2 - b^2 = (a - b)(a + b), where a = x and b = 3, since 3^2 = 9. So x^2 - 9 factors into (x - 3)(x + 3). Therefore (x - 3) is a factor.
Question 5: A system of equations is y = 2x + 1 and y = -x + 7. What is the solution?
- (2, 5) (Correct answer)
- (3, 4)
- (1, 3)
- (4, 3)
Correct answer: (2, 5)
Setting 2x + 1 = -x + 7 gives 3x = 6, so x = 2, and y = 2(2) + 1 = 5.
Since both equations equal y, set them equal: 2x + 1 = -x + 7. Add x to both sides: 3x + 1 = 7. Subtract 1: 3x = 6. Divide by 3: x = 2. Substitute back into y = 2x + 1: y = 2(2) + 1 = 5. The solution is (2, 5).
Question 6: What is the value of the function f(x) = x^2 - 2x + 1 when x = 3?
- 4 (Correct answer)
- 10
- 7
- 8
Correct answer: 4
f(3) = 3^2 - 2(3) + 1 = 9 - 6 + 1 = 4.
Substitute x = 3 into f(x) = x^2 - 2x + 1: f(3) = (3)^2 - 2(3) + 1 = 9 - 6 + 1 = 4. This function is actually a perfect square trinomial, (x-1)^2, and (3-1)^2 = 4, confirming the answer.
