Exercise 19 Page 155

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.

p + 1/4 ≥ 2

SubIneq

LHS-1/4≥RHS-1/4

p + 1/4 - 1/4 ≥ 2 - 1/4

WriteSum

Write as a sum

p + 1/4 - 1/4 ≥ 1 + 1 - 1/4

OneToFrac

Rewrite 1 as 4/4

p + 1/4 - 1/4 ≥ 1 + 4/4 - 1/4

SubFrac

Subtract fractions

p ≥ 1 + 3/4

AddTerms

Add terms

p ≥ 1 34

The above tells us that all values of p that are greater than or equal to 1 34 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that p can equal 1 34, which we show with a closed circle on the number line.