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Chapter 2: Q. 51 (page 112)

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

13w+54=w鈭�14

Short Answer

Expert verified

The value ofw=94

Step by step solution

01

Step 1. Given Information 

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

13w+54=w鈭�14

02

Step 2. The given equation is 13w +54=w−14

Now we solve the given equation for the value of w.

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 12.

1213w+54=12w鈭�14

Distribute.

12脳13w+12脳54=12脳w鈭�12脳144脳1w+3脳5=12w-3脳14w+15=12w-3

Simplify鈥攏otice, no more fractions.

Subtract by 4won both side

4w+15-4w=12w-3-4w15=8w-3

Add by 3on both side

15+3=8w-3+38w=1888w=188w=94

05

Step 5. Now checking the value.

Putting w=94in the given equation

13脳94+54=94鈭�1434+54=94鈭�143+54=9-1484=842=2

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