Exercise 45 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.

- 4 > - 4/3s

RearrangeIneq

Rearrange inequality

- 4/3s < - 4

MultEqn

LHS * (- 3/4)=RHS* (- 3/4)

- 4/3s(- 3/4) > - 4(- 3/4)

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Simplify left-hand side

CommutativePropMult

Commutative Property of Multiplication

- 4/3(- 3/4)s > - 4(- 3/4)

MultFracByInverse

a/b* b/a=1

1s > - 4(- 3/4)

IdPropMult

Identity Property of Multiplication

s > - 4(- 3/4)

MultNegNegOnePar

- a(- b)=a* b

s > 4( 3/4)

DenomMultFracToNumber

4 * a/4= a

s > 3

The above tells us that all values of s that are greater than 3 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that s cannot equal 3, which we show with an open circle on the number line.