Exercise 78 Page 407

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 must reverse the inequality sign.

1≥ - 8+x

AddIneq

LHS+8≥RHS+8

1+8≥ - 8+x+8

CommutativePropAdd

Commutative Property of Addition

1+8≥ - 8+8+x

AddTerms

Add terms

9≥ x

RearrangeIneq

Rearrange inequality

x≤ 9

The above tells us that all values of x that are less than or equal to 9 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can equal 9, which we show with a closed circle on the number line.

First, we can recall that inequalities can be solved in the same way as equations. We can do so 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.

x+81≤ 160

SubIneq

LHS-81≤RHS-81

x+81-81≤ 160-81

SubTerm

Subtract term

x≤ 79

The above tells us that all values of x that are less than or equal to 79 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can equal 79, which we show with a closed circle on the number line.