Question

What is the solution set for x in the equation, `5 - 4|-3x| = - 36`?

Answer 1

`x` can take the value `+-41/12`

Explanation:

Note that `|-3x|` is called an absolute value in that no matter what is inside the | | the result is always considered as a positive value.

To start with treat as a standard equation

If you wish you could do it this way:

Let `z=|-3x|`

Giving:

`5-4z=-36`

Subtract 5 from both sides

`-4z=-41`

`z=(-41)/(-4) = +41/4`
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But `z=|+-41/4| =|-3x|`

So `-3xx x=+-41/4`

Forgetting the signs for a moment

Consider `3x=41/4 =>x=41/12`

So `x` can take the value `+-41/12`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`|-3x| =|-3xx(+-41/12)|`