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Chapter 2: Q. 423 (page 196)

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

6x-3鈮�1and

5x-1>-6

Short Answer

Expert verified

The solution of the inequality:-1<x鈮�23

Interval notation:(-1,23]

The graph of the inequality on number line is:

Step by step solution

01

Step 1. Given Information.

We have:

6x-3鈮�1and

5x-1>-6

02

Step 2. Solve the inequality  

First, solve 6x-3鈮�1:

Add 3to the both sides:

6x-3+3鈮�鈥�1+36x鈮�鈥�46x6鈮�46x鈮�23

Interval notation: (-鈭�鈥�,鈥�23]

Now, solve 5x-1>鈥�-6:

Add 1to both sides:

5x-1+1>-6+15x>-55x5>-55x>-1

Interval notation:-1,鈥�鈭�鈥�

03

Step 3. Draw the solution on number line. 

Now, draw the solution x鈮�23and x>-1:

By combining both the inequalities, we get:

-1<x鈮�23

Interval notation:(-1,23]

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