Chapter ISG, Problem 5.4.1.2P

To determine

To solve the compound inequality.

  

Answer to Problem 5.4.1.2P

Solution set: $\left\{x|x<-1orx>3\right\}$

Interval notation: $(-\infty ,-1)\cup (3,\infty )$

Explanation of Solution

Given information:

Compound inequality

  

Calculation:

For Right −hand side,

  $-3x+7x-1<-5$

On solving,

  $4x-1<-5$

Adding one on both sides,

  $4x-1+1<-5+1$

On solving,

  $4x<-4$

Divide both sides by 4

  $\frac{4x}{4}<\frac{-4}{4}$

On solving,

  $x<-1$

For left-hand side,

  $-3x+7x-1>11$

On solving,

  $4x-1>11$

Add 1 both sides,

  $4x-1+1>11+1$

On solving,

  $4x>12$

Divide by 4 both sides

  $\frac{4x}{4}>\frac{12}{4}$

On solving,

  $x>3$

Hence, Solution set: $\left\{x|x<-1orx>3\right\}$

Graph of solution set is given below

  

Interval notation: $(-\infty ,-1)\cup (3,\infty )$