SAT Math Practice (Medium–Hard): Linear Equations, Systems & Functions (With Solutions)
- Tariq Malik
- 2 days ago
- 1 min read
Use this medium-to-hard practice set to build speed and accuracy. Try each question timed first, then review the step-by-step solution.
Question 1
If 3(2x − 5) = 4x + 7, what is the value of x?
A. 6
B. 7
C. 8
D. 9
Step-by-step solution
Distribute: 3(2x − 5) = 6x − 15.
Set equal: 6x − 15 = 4x + 7.
Subtract 4x from both sides: 2x − 15 = 7.
Add 15 to both sides: 2x = 22.
Divide by 2: x = 11.
Final answer: 11
Question 2
A system of equations is shown: y = 2x + 1 and y = −x + 10. What is the value of x at the intersection?
A. 3
B. 4
C. 5
D. 6
Step-by-step solution
At the intersection, the y-values are equal.
Set 2x + 1 = −x + 10.
Add x to both sides: 3x + 1 = 10.
Subtract 1: 3x = 9.
Divide by 3: x = 3.
Final answer: 3
Question 3
If f(x) = x^2 − 4x + 1, what is f(5)?
A. 6
B. 5
C. 4
D. 1
Step-by-step solution
Substitute x = 5 into the function.
f(5) = 5^2 − 4(5) + 1.
Compute: 25 − 20 + 1 = 6.
Final answer: 6
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