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Chapter 2: Q. 2.137 (page 200)

Solve3x-5-1=6

Short Answer

Expert verified

The required solutions arex1=-23鈥�,x2=4.

Step by step solution

01

Step 1. Given information. 

We have:

3x-5-1=6

02

Step 2. Isolate the absolute value expression 

We have:

3x-5-1=6

Add 1to both sides:

3x-5-1+1=6+13x-5=7

03

Step 4. Solve each equation 

Apply absolute rule: If鈥�|u|鈥�=鈥�a,鈥�a>0鈥�then鈥�u鈥�=鈥�a鈥�or鈥�u鈥�=鈥�-a

First, solve 3x-5=-7:

Add 5to both sides:

3x-5+5=-7+53x=-23x3=-23x=-23

Now, solve the second equation:

3x-5=7

Add 5to both sides:

3x-5+5=7+53x=123x3=123x=4

04

Step 4. Check the each solution 

Substitute -23and 4 into the original equation::

3x-5-1=6

At x=-23:

3-23-5-1=67-1=66=6

Hence, verified.

At x=4:

34-5-1=67-1=66=6

Hence, verified.

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