Question

How do you solve `-3y-2 = abs(6y + 25)`?

Answer 1

`color(red)(y = -3)` and `color(red)(y = -23/3)`.

Explanation:

We need to write two different equations without the absolute value symbols and solve for `y`.

These equations would be

(1) `−3y−2 = (6y+25)`
(2) `−3y−2= -(6y+25)`

Solve Equation 1:

`−3y−2 = 6y+25`

Add `3y` to each side.

`-2 = 9y + 25`

Subtract `25` from each side.

`-27 = 9y`

Divide each side by `3`.

`y = -3`

Solve Equation 2.

`−3y−2= -(6y+25)`

Remove parentheses.

`−3y−2= -6y-25`

Add `6y` to each side.

`3y-2 = -25`

Add 2 to each side.

`3y = -23`

Divide each side by `3`.

`y = -23/3`

The solutions are `y = -3` and `y = -23/3`.

Check:

If `y = -3`,

`−3y−2=|6y+25|`
`-3(-3) -2 = |6(-3) + 25|`
`9-2 = |-18+25|`
`7 =|7|`
`7=7`

If `y= -23/3`,

`−3y−2=|6y+25|`
`-3×(-23/3) -2 = |6×(-23/3) + 25|`
`23-2 = |-46+25|`
`21 =|-46 +25|`
`21= |-21|`
`21 = 21`