PSAT/NMSQT Math: Heart of Algebra 3

Question 1

If -2x + 7 < 3, what is the solution set?

Accepted Answer

x > 2

Answer

Subtract 7 to get -2x < -4, then divide by -2 and flip: x > 2.

Question 2

A function f(x) = 4x - 9. What is f(5)?

Accepted Answer

11

Answer

f(5) = 4(5) - 9 = 20 - 9 = 11.

Question 3

The system 2x + y = 7 and 2x + y = 10 has how many solutions?

Accepted Answer

None

Answer

Parallel lines with the same slope but different intercepts never intersect.

Question 4

If a + b = 12 and a - b = 4, what is a?

Accepted Answer

8

Answer

Adding the equations gives 2a = 16, so a = 8.

Question 5

Which value of x makes the equation 6x - 5 = 6x + 2 true?

Accepted Answer

No solution

Answer

Subtracting 6x gives -5 = 2, which is false, so there is no solution.

PSAT/NMSQT Practice Test