Question

How do you solve `\frac { 9} { 4} = \frac { 12} { 4x + 1}`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(4)color(blue)((4x + 1))` to eliminate the fractions while keeping the equation balanced. `color(red)(4)color(blue)((4x + 1))` is the Lowest Common Denominator of the two fractions:

`color(red)(4)color(blue)((4x + 1)) xx 9/4 = color(red)(4)color(blue)((4x + 1)) xx 12/(4x + 1)`

`cancel(color(red)(4))color(blue)((4x + 1)) xx 9/color(red)(cancel(color(black)(4))) = color(red)(4)cancel(color(blue)((4x + 1))) xx 12/color(blue)(cancel(color(black)(4x + 1)))`

`9(4x + 1) = 48`

Next, Expand the terms in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`(9 xx 4x) + (9 xx 1) = 48`

`36x + 9 = 48`

Then, subtract `color(red)(9)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`36x + 9 - color(red)(9) = 48 - color(red)(9)`

`36x + 0 = 39`

`36x = 39`

Now, divide each side of the equation by `color(red)(36)` to solve for `x` while keeping the equation balanced:

`(36x)/color(red)(36) = 39/color(red)(36)`

`(color(red)(cancel(color(black)(36)))x)/cancel(color(red)(36)) = (3 xx 13)/color(red)(3 xx 12)`

`x = (color(red)(cancel(color(black)(3))) xx 13)/color(red)(color(black)(cancel(color(red)(3))) xx 12)`

`x = 13/12`

Answer 2

`x=13/12`

Explanation:

Solve:

`9/4=(12)/(4x+1)`

Cross multiply the denominators.

`9(4x+1)=12xx4`

Expand.

`36x+9=12xx4`

Simplify.

`36x+9=48`

Subtract `9` from both sides.

`36x+color(red)cancel(color(black)(9))-color(red)cancel(color(black)(9))=48-9`

`36x=39`

Divide both sides by `36`.

`(color(red)cancel(color(black)(36))x)/color(red)cancel(color(black)(36))=39/36`

Simplify.

`x=39/36`

Reduce the fraction.

`3` goes into both `39` and `36`.

`x=(39-:3)/(36-:3)`

Simplify.

`x=13/12`