Exercise 43 Page 175

We can recall that 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 should reverse the inequality sign. We can consider our inequality. 6q < - 18 In this case, we can use the Division Property of Inequality. We can do so by dividing both sides of the inequality by 6. Let's do it!

6q < - 18

DivIneq

.LHS /6.<.RHS /6.

6q/6 < - 18/6

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Simplify left-hand side

MovePartNumRight

a* b/c=a/c* b

6/6q < - 18/6

QuotOne

a/a=1

1q < - 18/6

IdPropMult

Identity Property of Multiplication

q < - 18/6

MoveNegNumToFrac

Put minus sign in front of fraction

q < - 18/6

CalcQuot

Calculate quotient

q < - 3

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