Exercise 37 Page 301

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. We will begin by distributing 6 and 5 to remove the parentheses on both sides of the inequality. Now, we will use the Subtraction and Division Properties of Inequality to finish isolating m.

6m-18>10m+20

SubIneq

LHS-6m>RHS-6m

6m - 18 - 6m>10m+20-6m

SubTerms

Subtract terms

- 18 > 4m + 20

SubIneq

LHS-20>RHS-20

-18-20>4m+20-20

SubTerms

Subtract terms

- 38>4m

DivIneq

.LHS /4.>.RHS /4.

-38/4>4m/4

ReduceFrac

a/b=.a /4./.b /4.

-38/4>m/1

DivByOne

a/1=a

-38/4>m

MoveNegNumToFrac

Put minus sign in front of fraction

-38/4>m

WriteDec

Write as a decimal

-9.5>m

RearrangeIneq

Rearrange inequality

m<-9.5

Now, we can write the solution set. {m|m<-9.5}