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Chapter 2: Q. 421 (page 196)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:

15x-5+6<4and 3-23x<5

Short Answer

Expert verified

The solution of the inequality: -鈭�鈥�,鈥�-5and -3,鈥�鈭�鈥�

Interval notation:-5,-3

The graph of the inequality on number line is

Step by step solution

01

Step 1. Given Information. 

We have:

15x-5+6<4and

3-23x<5

02

Step 2. Solve the inequality. 

First, solve 15x-5+6<鈥�4:

Subtract 6from both sides:

15x-5+6-6<4-615x-5<-25路15x-5<5-2x-5<-10x-5+5<-10+5x<-5

Internal notation: -鈭�鈥�,鈥�-5

Now, solve 3-23x<鈥�5:

Subtract 3from both sides:

3-23x-3<5-3-23x<2

Multiply both sides by -1(reverse the inequality):

-23x-1>2-123x>-23路23x>3-22x>-62x2>-62x>-3

Interval notation:-3,鈥�鈭�鈥�

03

Step 3. Draw the solution on the number line. 

Draw the solution -鈭�,-5and -3,+鈭�on the number line:

By combining the both solutions, we get:

-5,-3

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