Question

How do you solve `\frac { x - 3} { 2} = \frac { 3x + 1} { 4}`?

Answer 1

`x = -7`

Explanation:

`4(x - 3) = 2(3x + 1)`
`rArr 2(x - 3) = 3x + 1`
`rArr 2x - 6 = 3x + 1`
`rArr -6 - 1 = 3x - 2x`

`therefore x = -7`

Answer 2

`x=-7`

Explanation:

`color(green)((x-3)/2color(red)(xx1)" "=" "(3x+1)/4)`

`color(green)((x-3)/2color(red)(xx2/2)" "=" "(3x+1)/4)`

`color(green)((color(red)(2)(x-3))/(2color(red)(xx2))" "=" "(3x+1)/4)`

`(2x-6)/4=(3x+1)/4`

Two ways of looking at the next step

Concept 1: multiply both sides by 4

Concept 2: As the denominators are the same then we only need to consider the numerators.

`2x-6=3x+1`

Subtract `2x` from both sides

`-6=x+1`

Subtract 1 from both sides

`-7=x`

`x=-7`
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Check:

`(x-3)/2 = (3x+1)/4`

`(-7-3)/2=(-21+1)/4`

`" "-5" "=" "-5`