Exercise 28 Page 396

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.

5x/8 ≥ 30

MultIneq

LHS* 8 ≥ RHS * 8

5x/8 * 8 ≥ 30 * 8

FracMultDenomToNumber

a/8* 8 = a

5x ≥ 30* 8

Multiply

Multiply

5x ≥ 240

DivIneq

.LHS /5.≥.RHS /5.

5x/5 ≥ 240/5

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Calculate quotient

MovePartNumRight

a* b/c=a/c* b

5/5x≥ 240/5

QuotOne

a/a=1

1x≥ 240/5

IdPropMult

Identity Property of Multiplication

x≥ 240/5

CalcQuot

Calculate quotient

x ≥ 48

Note that all values of x greater than or equal to 48 satisfy the inequality. Now let’s graph the inequality on a number line. Since x is all values greater than or equal to 48, we will shade to the right of our point at 48, including 48 with the closed circle.