Exercise 28 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.

c + 1 14 < 5

SubIneq

LHS-1 14

c + 1 14 - 1 14 < 5 - 1 14

SubTerm

Subtract term

c < 5 - 1 14

▼

Simplify right-hand side

WriteSum

Write as a sum

c < 4 + 1 - 1 14

OneToFrac

Rewrite 1 as 4/4

c < 4 + 4/4 - 1 14

WriteDiff

Write as a difference

c < 4 + 4/4 - 1 - 1/4

SubTerms

Subtract terms

c< 3 + 3/4

AddTerms

Add terms

c< 3 34

The above tells us that all values of c that are less than 3 34 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that c can not equal 3 34, which we show with an open circle on the number line.