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Chapter 2: Q. 52 (page 112)

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

12a鈭�14=16a+112

Short Answer

Expert verified

The value ofa=1

Step by step solution

01

Step 1. Given Information 

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

12a鈭�14=16a+112

02

Step 2. The given equation is 12a−14=16a+112

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

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 are2,4,6,12

So the LCD is12

04

Step 4. Multiply both sides of the equation by 12.

1212a鈭�14=1216a+112

Distribute.

12脳12a鈭�12脳14=12脳16a+12脳1126a-3=2a+1

Simplify鈥攏otice, no more fractions.

Subtract 2aon both side

6a-3-2a=2a+1-2a4a-3=1

Add 3 on both side

4a-3+3=1+34a=444a=44a=1

05

Step 5. Now checking the value.

Putting a=1in the given equation

12脳1鈭�14=16脳1+11212-14=16+11212脳22-14=16脳22+11224-14=212+1122-14=2+11214=31214=14

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