Question

Solve: `y + y/2 = 7/4 - y/4`

Answer 1

`y + y/2 = 7/4 - y/4`

⇒ `y/1 + y/2 = 7/4 - y/4`

⇒  `(4y + 2y = 7 - y)/4`

⇒ 4y + 2y = 7 - y

⇒  4y + 2y ⇒ 7y = 7

⇒ y = `7/7 = 1`

∴ y = 1

Answer 2

`y + y/2 = 7/4 - y/4`

`y + y/2 = (2y)/2 + y/2 = (3y)/2`

The equation now becomes:

`(3y)/2 = 7/4 - y/4`

Combine terms on the right-hand side

`7/4 - y/4 = (7-y)/4`

`(3y)/2 = (7-y)/4`

Multiply through by the least common denominator (LCD), which is 4:

`4xx (3y)/2 = 4xx (7-y)/4`

2 × 3y = 7 − y.

6y = 7 − y

Add y to both sides to isolate y terms on one side: 6y + y = 7

7y = 7

Divide both sides by 7

y = 1.