Question

this series of problems will build your fluency with solving compound inequalities. for each question below, find the solution and graph your answer on a number line.

use the answer key to determine that you accurately identified each solution.

if necessary, revise your work.

1. 9≤x - 5≤11

Explanation:

Step1: Add 5 to all parts

Add 5 to each part of the compound - inequality \(9\leq x - 5\leq11\).
\[9+5\leq x-5 + 5\leq11 + 5\]

Step2: Simplify the inequality

Simplify the left - hand side, middle, and right - hand side of the inequality.
\[14\leq x\leq16\]

Answer:

The solution of the compound inequality is \(14\leq x\leq16\). On a number line, you would draw a solid circle at \(x = 14\) and \(x = 16\) and shade the region between them.