Exercise 3 Page 329

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.

2x-5< 9

AddIneq

LHS+5

2x-5+5< 9+ 5

AddTerms

Add terms

2x< 14

DivIneq

.LHS /2.<.RHS /2.

2x/2< 14/2

MovePartNumRight

a* b/c=a/c* b

2/2x<14/2

CalcQuot

Calculate quotient

x< 7

The above tells us that all values of x that are less than 7 will satisfy the inequality. Let's demonstrate the inequality by graphing the solution set on a number line. Notice that x cannot be equal to 7, which we show with an open circle on the number line.