Question

How do you solve `\frac { 2} { 4x + 1} = \frac { - 3} { x - 8}`?

Answer 1

`x = 13/14`

Explanation:

Given: `2/(4x + 1) = (-3)/(x-8)`

One way is to multiply the equation by the common denominator.

Common denominator `= (4x+1)(x-8)`

`cancel(4x+1)(x-8) * 2/cancel(4x + 1) = (4x+1)cancel(x-8) * (-3)/cancel(x-8)`

This reduces to `" "2(x-8) = -3(4x+1)`

Distribute: `" "2x - 16 = -12x -3`

Add `12x` on both sides: `" "14x - 16 = -3`

Add `16` on both sides: `" "14x = 13`

`x = 13/14`

CHECK:

`2/(4/1 * 13/14 + 1) = 2/(52/14 + 14/14) = 2/(66/14) = 2/1 * 14/66 = 28/66 = 14/33`

`(-3)/(13/14 - 8/1*14/14) = (-3)/(13/14 - 112/14)= (-3)/(-99/14) = 3/1 * 14/99 = 42/99 = 14/33`