Question

use the addition property of inequality to solve the inequality and graph the solution on a number line.
x - 5 > 3
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is \boxed{}.
(type your answer in interval notation.)
b. the solution set is \varnothing, the empty set.

Explanation:

Step1: Apply addition property

Add 5 to both sides of the inequality \( x - 5 > 3 \) to isolate \( x \). By the addition property of inequality, adding the same number to both sides preserves the inequality. So we have \( x - 5 + 5 > 3 + 5 \).

Step2: Simplify both sides

Simplifying the left side: \( x - 5 + 5 = x \). Simplifying the right side: \( 3 + 5 = 8 \). So the inequality becomes \( x > 8 \).

Step3: Write in interval notation

The solution \( x > 8 \) in interval notation is \( (8, \infty) \).

Answer:

A. The solution set is \((8, \infty)\).