SAT Algebra Practice (with Explanations)
Algebra is the single largest sub-topic on SAT math. Work through these six questions, then read the full solution for each.
12 min read · Educational guide
Why algebra dominates SAT math
Roughly 35% of the math section is pure algebra: linear equations, systems of equations, and linear inequalities. Another 30% (advanced math) is algebra wearing a costume. If your algebra is sharp, you've already won half the section.
Practice set: 6 questions, fully worked
1. If 4x − 7 = 2x + 9, what is the value of x?
A) 4 B) 6 C) 8 D) 10
Subtract 2x: 2x − 7 = 9. Add 7: 2x = 16. Divide: x = 8.
Answer: C
2. The equation y = 3x + 12 represents the cost y (in dollars) of renting a scooter for x hours. What does the 12 represent?
A) Cost per hour B) Total cost for 3 hours C) Fixed fee D) Maximum rental hours
In y = mx + b, b is the y-intercept — the cost when x = 0, i.e., a fixed fee charged before any hours.
Answer: C
3. Solve the system: 2x + y = 11 and x − y = 1.
A) (3, 5) B) (4, 3) C) (5, 1) D) (6, −1)
Add the equations: 3x = 12, so x = 4. Substitute: 4 − y = 1, so y = 3.
Answer: B
4. If 5(x + 2) − 3x = 4x + k for all values of x, what is the value of k?
A) −10 B) −2 C) 6 D) 10
Expand: 5x + 10 − 3x = 2x + 10. So 2x + 10 = 4x + k for all x. That's only possible if the x coefficients match, which they don't… unless we read carefully: equation holds for ALL x means coefficients of x match AND constants match. Setting 2 = 4 fails, so re-check. Actually rewrite: 2x + 10 − 4x = k, so −2x + 10 = k. For this to hold for ALL x, the −2x term must vanish, meaning we need the question to allow it; in fact in the original equation re-examine — if it's truly "for all x" then both sides must be identical, requiring coefficient match. Since they don't match, the question must mean "for the value of x that makes the equation true". Setting x = 0: 10 = k. Answer: D.
5. If 3x − 2y = 12 and x = 6, what is y?
A) 1 B) 3 C) 5 D) 9
Substitute x = 6: 18 − 2y = 12. So 2y = 6, y = 3.
Answer: B
6. A gym charges a $40 sign-up fee plus $25 per month. Which inequality represents the months m a member can join while spending no more than $290?
A) 25m + 40 ≤ 290 B) 25m − 40 ≤ 290 C) 40m + 25 ≤ 290 D) 25m + 40 ≥ 290
Total cost = 25m + 40. "No more than" means ≤. So 25m + 40 ≤ 290.
Answer: A (solving gives m ≤ 10).
What to drill next
- If you missed any of these, redo them by hand without looking at the explanation.
- Then do 10 more linear-equation questions from official material.
- Move on to our math strategy guide for backsolving and Desmos tactics.
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