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Chapter 2: Q. 56 (page 112)

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

15(q+3)=12(q-3)

Short Answer

Expert verified

The value ofq=7

Step by step solution

01

Step 1. Given Information 

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

15(q+3)=12(q-3)

02

Step 2. The given equation is 15(q+3)=12(q-3)

Now we solve the given equation for the value ofq

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.

15脳10(q+3)=12脳10(q-3)2(q+3)=5(q-3)

Distribute.

2脳q+2脳3=5脳q-5脳32q+6=5q-15

05

Step 5. Simplify—notice, no more fractions. 

Subtract2qon both side

2q+6-2q=5q-15-2q3q-15=6

Add 15on both side

3q-15+15=6+153q=2133q=213q=7

06

Step 6. Now checking the value. 

Putting q=7in the given equation

15(7+3)=12(7-3)15(10)=12(4)2=2

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