Question

What is 1/3a-1/4=5/6-3/2

Answer 1

The value of "a" is a = -1.25 or
`(-5)/(4)`

Solution:

Given expression is:

`(1)/(3)a - (1)/(4) = (5)/(6) - (3)/(2)`

We have to solve the above expression for "a"

`(a)/(3) - (1)/(4) = (5)/(6) - (3)/(2)`

Take L.C.M of denominators of L.H.S and R.H.S

L.C.M of 3 and 4:

List all prime factors for each number.

Prime factor of 3 = 3

Prime factor of 4 = 2 x 2

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 = 12

L.C.M of 6 and 2:

Prime factor of 6 = 2 x 3

Prime factor of 2 = 2

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 3

Multiply these factors together to find the LCM.

LCM = 2 x 3 = 6

Now make the denominators same

`(a)/(3) - (1)/(4) = (5)/(6) - (3)/(2)\\\\(a * 4)/(3 * 4) - (1 * 3)/(4 * 3) = (5 * 1)/(6 * 1) - (3 * 3)/(2 * 3)\\\\(4a)/(12)-(3)/(12) = (5)/(6)-(9)/(6)\\\\(4a - 3)/(12) = (5-9)/(6)`

Simplify the above expression

`(4a - 3)/(12) = (5-9)/(6)\\\\4a - 3 = 2(-4)\\\\4a - 3 = -8\\\\4a = -8 + 3\\\\4a = -5\\\\a = (-5)/(4)`

Thus value of "a" is a = -1.25 or
`(-5)/(4)`