Exercise 6 Page 153

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.

x + 3/4 > 1 12

SubIneq

LHS-3/4>RHS-3/4

x + 3/4 - 3/4 > 1 12 - 3/4

AddTerms

Add terms

x > 1 12 - 3/4

▼

Simplify right-hand side

WriteSum

Write as a sum

x > 1 + 1/2 - 3/4

OneToFrac

Rewrite 1 as 4/4

x > 4/4 + 1/2 - 3/4

CommutativePropAdd

Commutative Property of Addition

x > 1/2 + 4/4 - 3/4

SubFrac

Subtract fractions

x > 1/2 + 1/4

ExpandFrac

a/b=a * 2/b * 2

x > 2/4 + 1/4

AddFrac

Add fractions

x > 3/4

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