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Chapter 2: Q. 2.138 (page 199)

Solve4x-3-5=2

Short Answer

Expert verified

The required solutions arex1=-1,x2=52.

Step by step solution

01

Step 1. Given information.  

We have:

4x-3-5=2

02

Step 2. Isolate the absolute expression. 

We have:

4x-3-5=2

Add 5to both sides:

4x-3-5+5=2+54x-3=7

03

Step 3. Write the equivalent equations. 

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

4x-3=-7or鈥�4x-3=7

04

Step 4. Solve the each equations. 

Start with first equation:

4x-3=-7

Add 3to both sides:

4x-3+3=-7+34x=-44x4=-44x=-1

Now, solve the second equation:

4x-3=7

Add 3to both sides:

4x-3+3=7+34x=104x4=104x=52

05

Step 5. Check the each solution. 

Substitute -1and 52into the original equation:

4x-3-5=2

At x=-1:

4-1-3-5=27-5=22=2

Hence, verified.

At x=52:

452-3-5=27-5=22=2

Hence, verified.

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