Exercise 27 Page 503

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. Let's use the Subtraction Property of Inequality to solve the inequality.

6 ≥ x + 3 13

SubIneq

LHS-3 13≥RHS-3 13

6 - 3 13 ≥ x + 3 13 - 3 13

SubTerm

Subtract term

6 - 3 13 ≥ x

▼

Simplify left-hand side

WriteSum

Write as a sum

2 + 1 - 3 13 ≥ x

OneToFrac

Rewrite 1 as 3/3

2 + 3/3 - 3 13 ≥ x

WriteDiff

Write as a difference

2 + 3/3 - 3 - 1/3≥ x

SubTerms

Subtract terms

- 1 + 2/3 ≥ x

AddTerms

Add terms

- 1/3≥ x

RearrangeIneq

Rearrange inequality

x ≤ - 1/3

The above tells us that all values of x that are less than or equal to - 13 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can equal - 13, which we show with a closed circle on the number line.