Question

How do you solve `7-3abs(4d-7)=4`?

Answer 1

`d=2` or `d=3/2`

Explanation:

Your absolute value equation looks like this

`7 - 3|4d-7| = 4`

Start by isolating the modulus on one side of the equation

`color(red)(cancel(color(black)(7))) - color(red)(cancel(color(black)(7))) - 3|4d-7| = 4 - 7`

`(color(red)(cancel(color(black)(-3))) * |4d-7|)/color(red)(cancel(color(black)(-3))) = (-3)/(-3)`

`|4d-7| = 1`

Now, this equation will produce two values for `d`, depending on which condition is true

• If `(4d-7)>0`, then you have

`|4d-7| = 4d-7`

and the equation becomes

`4d-7 = 1 => d = 8/4 = color(green)(2)`

• If `(4d-7)<0`, then you have

`|4d-7| = -(4d-7) = -4d + 7`

This will get you

`-4d+7 = 1 => d = 6/4 = color(green)(3/2)`