Exercise 52 Page 175

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 we divide or multiply by a negative number, we must reverse the inequality sign.

- 1/3(p+9)≤ 4

DivIneq

.LHS /(- 1/3).≤.RHS /(- 1/3).

- 13(p+9)/- 13≥4/- 13

▼

Simplify left-hand side

MovePartNumRight

a* b/c=a/c* b

- 13/- 13(p+9)≥4/- 13

QuotOne

a/a=1

1(p+9)≥4/- 13

IdPropMult

Identity Property of Multiplication

(p+9)≥4/- 13

RemovePar

Remove parentheses

p+9≥4/- 13

DivByFracSL

.a /b/c.=a* c/b

p+9≥ - 4*3/1

Multiply

Multiply

p+9≥ - 12/1

QuotOne

a/a=1

p+9≥ - 12

SubEqn

LHS-9=RHS-9

p≥ - 21

The above tells us that all values of p that are greater than or equal to - 21 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that p can equal - 21, which we show with a closed circle on the number line.