Question

-2|10w-8|+9=-15

solve the equation??

Answer 1

Hi there,

I hope you and your family are staying safe and healthy!

Let's Solve the Equation

`-2|10w-8|+9=-15`

Let's start by adding -9 to both sides

`-2(|10w-8|)+9+-9=-15+-9\\-2(|10w-8|)=-24`

Now we divide both sides by -2

`(-2(|10w-8|))/(-2) = (-24)/(-2) \\|10w-8|=12`

Almost there! SO now we need to solve for the absolute value.

So we know either
`10w - 8 = 12` or
`10w - 8 = -12`

Thus, we can say that we have two possibilities here. So we need to solve them both.

Possibility #1

`10w-8=12 \\10w = 12+8\\\\10w = 20 \\w = (20)/(10) \\w = 2`

Possibility #2

`10w - 8 = -12 \\10w = -12 + 8\\10w = -4 \\w = (-4)/(10) \\w = (-2)/(5)`

The answer is:
`w = 2` or
`w = (-2)/(5)`

I wish you all the best this semester!

~Garebear