Question

Can someone help me with this please, it is late and my mind is just gone :)

Answer 1

`w=-1/5\text{ or } 3`

Explanation:

We have the equation:

`-2|5w-7|+9=-7`

Let's first isolate the absolute value. Subtract 9 from both sides:

`-2|5w-7|=-16`

Divide both sides by -2:

`|5w-7|=8`

Now, we can split them into two cases. By the definition of absolute value:

`5w-7=8\text{ or } -(5w-7)=8`

Let's do each case individually.

Case 1:

We have:

`5w-7=8`

Add 7 to both sides:

`5w=15`

Divide both sides by 5:

`w=3`

Case 2:

We have:

`-(5w-7)=8`

Divide both sides by -1:

`5w-7=-8`

Add 7 to both sides:

`5w=-1`

Divide both sides by 5:

`w=-1/5`

So, our answers are:

`w=-1/5\text{ or } 3`

And we're done!