Exercise 7 Page 394

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.

3/2m > 1

MultIneq

LHS* 2 > RHS * 2

3/2m* 2 > 1* 2

CommutativePropMult

Commutative Property of Multiplication

3/2* 2m > 1* 2

NumberToDenomMultFrac

a = 2 * a/2

3m> 1* 2

IdPropMult

Identity Property of Multiplication

3m> 2

DivIneq

.LHS /3.>.RHS /3.

3m/3 > 2/3

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Calculate quotient

MovePartNumRight

a* b/c=a/c* b

3/3m > 2/3

QuotOne

a/a=1

1m > 2/3

IdPropMult

Identity Property of Multiplication

m > 2/3

We found that all values of m greater than 23 will satisfy the inequality. Now let’s graph the inequality on a number line. Since m cannot equal 23, we draw an open circle at this point. Since m is all values greater than 23, we will shade the part of the number line that represents numbers greater than 23. This means that we shade to the right of our point at 23.