Question

How do you solve `\frac { 11x } { 4} - 9= \frac { x } { 2} + 45`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(9)` and subtract `color(blue)(x/2)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(blue)(x/2) + (11x)/4 - 9 + color(red)(9) = -color(blue)(x/2) + x/2 + 45 + color(red)(9)`

`-color(blue)(x/2) + (11x)/4 - 0 = 0 + 54`

`-x/2 + (11x)/4 = 54`

Next, put the fractions on the left side of the equation over common denominators and perform the addition:

`(2/2 xx -x/2) + (11x)/4 = 54`

`(-2x)/4 + (11x)/4 = 54`

`(-2x + 11x)/4 = 54`

`((-2 + 11)x)/4 = 54`

`(9x)/4 = 54`

Now, multiply each side of the equation by `color(red)(4)/color(blue)(9)` to solve for `x` while keeping the equation balanced:

`color(red)(4)/color(blue)(9) xx (9x)/4 = color(red)(4)/color(blue)(9) xx 54`

`cancel(color(red)(4))/cancel(color(blue)(9)) xx (color(blue)(cancel(color(black)(9)))x)/color(red)(cancel(color(black)(4))) = color(red)(4)/cancel(color(blue)(9)) xx color(blue)(cancel(color(black)(54)))6`

`x = 24`

Answer 2

`color(brown)(x=24`

Explanation:

`(11x)/4-9=x/2+45`

multiply both sides by 4

`:.11x-36=2x+180`

`:.11x-2x=180+36`

`:.9x=216`

`:.x=216/9`

`:.color(brown)(x=24`

substitute `color(brown)(x=24`

`:.(11(color(brown)24))/4-9=((color(brown)24))/2+45`

`:.264/4-9=12+45`

`:.66-9=57`

`:.color(brown)(57=57`