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Chapter 2: Q. 53 (page 112)

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

13b+15=25b鈭�35

Short Answer

Expert verified

The value ofb=12

Step by step solution

01

Step 1. Given Information 

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

13b+15=25b鈭�35

02

Step 2. The given equation is 13b+15=25b−35

Now we solve the given equation for the value ofb

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 are3,5

So the LCD is15

04

Step 4. Multiply both sides of the equation by 15.

1513b+15=1525b鈭�35

Distribute.

15脳13b+15脳15=15脳25b鈭�15脳355脳1b+3脳1=3脳2b-3脳35b+3=6b-9

05

Step 5. Simplify—notice, no more fractions. 

Subtract by 5bon both side

5b+3-5b=6b-9-5bb-9=3

Add by 9 on both side

b-9+9=3+9b=12

06

Step 6. Now checking the value. 

Putting b=12in the given equation

13脳12+15=25脳12鈭�354+15=245鈭�354脳55+15=24-3520+15=215215=215

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