Keystone Test Algebra: Linear Equations/Inequalities 5

Question 1

Solve: |x − 3| = 7

Accepted Answer

x = 10 or x = −4

Answer

The absolute value equation gives x − 3 = 7 (x = 10) or x − 3 = −7 (x = −4).

Question 2

A bus travels at a constant speed. It covers 180 miles in 3 hours. Which equation gives the distance d after t hours?

Accepted Answer

d = 60t

Answer

Speed = 180 ÷ 3 = 60 mph, so the linear equation is d = 60t.

Question 3

For which value of k does the equation 3x + k = 3x − 5 have no solution?

Accepted Answer

Any k ≠ −5

Answer

Subtracting 3x gives k = −5; this is only true when k = −5, so any other value of k makes it a contradiction with no solution.

Question 4

A student scored 78, 85, and 91 on three tests. What score s on the fourth test gives an average of at least 85?

Accepted Answer

s ≥ 86

Answer

Set up (78 + 85 + 91 + s)/4 ≥ 85; the sum is 254 + s ≥ 340, so s ≥ 86.

Question 5

What is the solution to the system of equations if they graph as two parallel lines?

Accepted Answer

No solution

Answer

Parallel lines never intersect, so the system has no solution.

Keystone Test Practice Test