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Question
Solve: `y + y/2 = 7/4 - y/4`
Solution 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
Solution 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.
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