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Chapter 2: Q. 59 (page 112)

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

4n+84=n3

Short Answer

Expert verified

The value ofn=-3

Step by step solution

01

Step 1. Given Information 

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

4n+84=n3

02

Step 2. The given equation is 4n+84=n3

Now we solve the given equation for the value ofn

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 are3,4

So the LCD is12

04

Step 4. Multiply both sides of the equation by .

4n+84脳12=n3脳1234n+8=4n

Distribute.

3脳4n+3脳8=4n12n+24=4n

05

Step 5. Simplify—notice, no more fractions. 

Subtract 4non both side

12n+24-4n=4n-4n8n+24=0

Subtract 24 on both side

8n+24-24=0-248n=-2488n=-248n=-3

06

Step 6. Now checking the value. 

Putting n=-3in the given equation

role="math" localid="1645452753493" 4(-3)+84=-33-12+84=-1-44=-1-1=-1

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