Question

How do you solve `(x+1)/3 = (2x-1)/4`?

Answer 1

`x=7/2`

Explanation:

`"multiply both sides by the lowest common multiple of"`
`"3 and 4 that is 12"`

`cancel(12)^4xx(x+1)/cancel(3)^1=cancel(12)^3xx(2x-1)/cancel(4)^1`

`4(x+1)=3(2x-1)larrcolor(blue)"distribute"`

`4x+4=6x-3`

`"subtract "4x" from both sides"`

`4=2x-3`

`"add 3 to both sides and divide by 2"`

`7=2xrArrx=7/2`

`color(blue)"As a check"`

`"left "=(7/2+2/2)/3=(9/2)/3=9/6=3/2`

`"right "=(14/2-2/2)/4=6/4=3/2`

`x=7/2" is the solution"`

Answer 2

`x = 7/2`

Explanation:

Multiply both sides by `12`:

`cancel(12)^4\frac{x+1}{cancel(3)} = \frac{2x-1}{cancel(4)}cancel(12)^3`

So, the equation becomes

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

Expand both sides to get

`4x+4 = 6x-3`

Subtract `6x` to both sides:

`-2x+4=-3`

Subtract `4` from both sides:

`-2x = -7`

Divide both sides by `-2`:

`x = 7/2`