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Chapter 2: Q. 2.140 (page 201)

Solve2x-5+3=9

Short Answer

Expert verified

The required solutions arex1=2,x2=8.

Step by step solution

01

Step 1. Given information 

We have:

2x-5+3=9

02

Step 2. Isolate the absolute expression. 

We have:

2x-5+3=9

Subtract 3from both sides:

2x-5+3-3=9-32x-5=62x-52=62x-5=3

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

x-5=-3or鈥�x-5=3

04

Step 4. Solve the each equations. 

Start with first equation:

x-5=-3

Add 5to both sides:

x-5+5=-3+5x=2

Now, solve second equation:

x-5=3

Add 5to both sides:

x-5+5=3+5x=8

05

Step 5. Check the each solution. 

Substitute 2and 8into the original equation:

2x-5+3=9

At x=2:

22-5+3=96+3=99=9

Hence, verified.

At x=8:

28-5+3=96+3=99=9

Hence, verified.

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