Exercise 10 Page 215

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.

7w+12 ≥ 2w-3

AddIneq

LHS+3≥RHS+3

7w+15 ≥ 2w

SubIneq

LHS-7w≥RHS-7w

15 ≥ -5w

DivNegIneq

Divide by - 5 and flip inequality sign

-3 ≤ w

RearrangeIneq

Rearrange inequality

w ≥ - 3

This inequality tells us that all values greater than or equal to - 3 will satisfy the inequality.

Below we demonstrate the inequality by graphing the solution set on a number line. Notice that w can equal - 3, which we show with a closed circle on the number line.