Problem

Solve the following inequality and graph the solution set on a number line. \[ 22(x+1)-43<21 x+1 \] What is the solution set? \[ \{x \mid \square \text { (Type an inequality.) } \] What is the graph of the solution set? A. B. c. D.

Solution

Step 1 :First, distribute the 22 in the left side of the inequality: \(22x + 22 - 43 < 21x + 1\).

Step 2 :Simplify the left side of the inequality: \(22x - 21 < 21x + 1\).

Step 3 :Subtract \(21x\) from both sides of the inequality: \(x - 21 < 1\).

Step 4 :Add 21 to both sides of the inequality: \(x < 22\).

Step 5 :The solution set is \(\{x \mid x < 22\}\).

Step 6 :To graph the solution set, draw a number line and shade all numbers less than 22. The graph should have an open circle at 22 and the shading should extend to the left of 22.

From Solvely APP
Source: https://solvelyapp.com/problems/18919/

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