Chapter ISG, Problem 5.4.2.8P

To determine

To solve the inequality.

  

Answer to Problem 5.4.2.8P

Solution set is $\left\{x\right|x>-4or-3\le 2x+1\le 5\}$

The graph of inequality $5-3x<17OR-3\le 2x+1\le 5$

Explanation of Solution

Given information:

Inequality

  $5-3x<17OR-3\le 2x+1\le 5$

Calculation:

  $5-3x<17OR-3\le 2x+1\le 5$

First half of compound inequality is $5-3x<17$ and second half is $-3\le 2x+1\le 5$

Solving for first half

  $5-3x<17$

Subtracting 5 from both sides

  $5-3x-5<17-5$

On solving,

  $-3x<12$

Dividing by 3 both sides

  

On solving,

  $-x<4$

Multiply by -1 both sides,

  $x>-4$

Solving for second half

  

Subtracting 1 from all sides

  

On solving,

  

Dividing by 2 all sides

  

On solving,

  

Solution set of second half: $\left\{x\right|-2\le x\cap x\le 2\}$

The graph of inequalities is given below

x>-4

  

  

  

Solution set is $\left\{x\right|x>-4or-3\le 2x+1\le 5\}$

The graph of inequality $5-3x<17OR-3\le 2x+1\le 5$