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Chapter 2: Q. 64 (page 112)

In the following exercises, solve each equation with fraction coefficients.

3v鈭�62+5=11v鈭�45

Short Answer

Expert verified

The value ofv=4

Step by step solution

01

Step 1. Given Information 

In the given question we have to solve equation with fraction coefficients.

3v鈭�62+5=11v鈭�45

02

Step 2. The given equation is 3v−62+5=11v−45

Now we solve the given equation for the value ofv

03

Step 3. We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation. 

Finding the LCD of all fractions in the equation.

The numbers are2,5

So the LCD is10

04

Step 4. Multiply both sides of the equation by 10.

103v鈭�62+5=1011v鈭�45

Distribute.

role="math" localid="1645456240112" 10脳3v鈭�62+10脳5=511v鈭�45(3v鈭�6)+50=211v鈭�415v鈭�30+50=22v鈭�815v+20=22v鈭�8

05

Step 5. Simplify—notice, no more fractions. 

Subtract on both side

15v+20-15v=22v鈭�8-15v7v-8=20

Add 8 on both side

7v-8+8=20+87v=2877v=287v=4

06

Step 6. Now checking the value. 

Putting v=4in the given equation

role="math" localid="1645456429363" 3脳4鈭�62+5=11脳4鈭�4512鈭�62+5=44鈭�4562+5=4053+5=88=8

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