Question

The inequality −4(x − 2) < 24 is given.

Part A: Solve the inequality and show every step of your work.

Part B: Explain in words how to graph the solution to the inequality on a number line.

Part C: Find two values that would make the inequality true. Explain how you know the values are solutions to the inequality.

Answer 1

Explanation:

A.

−4(x − 2) < 24

-4x + 8 < 24

-4x < 24 - 8

-4x < 16

x > -4 (Note that the sign is flipped as we are dividing by a negative).

B.

Draw the graph of x = -4 ( it will be a vertical dotted line passing through -4 on the x axis) and shade to the left of the dotted line.

C.

Every x value to the left of x = -4 will be a solution to the inequality.

So, x = -5 and x = -7 are 2 solutions.