Question

How do you solve `-6abs(5-2y) = -9`?

Answer 1

`y = 7/4" "` or `" "y = 13/4`

Explanation:

Start by isolating the modulus on one side of the equation. This can be done by dividing both sides by `-6`

`(color(red)(cancel(color(black)(-6))) * |5 - 2y|)/color(red)(cancel(color(black)(-6))) = ((-9))/((-6)`

`|5 - 2y| = 3/2`

Since you're dealing with the absolute value of an expression, you must take into account the fact that the expression can be negative or positive.

• `5-2y>0 implies |5-2y| = 5 - 2y`

Your equation becomes

`5 - 2y = 3/2`

`2y = 5 - 3/2`

`y = (10 - 3)/2 * 1/2 = color(green)(7/4)`

• `5 - 2y <0 implies |5 - 2y| = -(5-2y)`

This time, the equation becomes

`-(5 - 2y) = 3/2`

`-5 + 2y = 3/2`

`2y = (3 + 10)/2`

`y = 13/2 * 1/2 = color(green)(13/4)`

Your original equation has two possible solutions,

`y = 7/4" "` or `" "y = 13/4`