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Chapter 2: Q. 54 (page 112)

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

13x+25=15x鈭�25

Short Answer

Expert verified

The value ofx=-6

Step by step solution

01

Step 1. Given Information 

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

13x+25=15x鈭�25

02

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

Now we solve the given equation for the value ofx

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.

1513x+25=1515x鈭�25

Distribute.

15脳13x+15脳25=15脳15x鈭�15脳255脳1x+3脳2=3脳1x-3脳25x+6=3x-6

05

Step 5. Simplify—notice, no more fractions. 

Subtract by 3xon both side

localid="1645447548615" 5x+6-3x=3x-6-3x2x+6=-6

Subtract 6 on both side

2x+6-6=-6-62x=-1222x=-122x=-6

06

Step 6. Now checking the value. 

Putting x=-6in the given equation

13(-6)+25=15(-6)鈭�25-2+25=-65-25-2路55+25=-65-25-105+25=-65-25-10+25=-6-25-85=-85

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