Question

How do you solve `-7abs(-3-3r)=-21`?

Answer 1

The solution set is `{0, -2}`.

Explanation:

Let's first isolate the absolute value on one side of the equation.

`|-3 - 3r| = -21/-7`

`|-3 - 3r| = 3`

Now, when dealing with absolute value equations, we must consider two scenarios.

A: The absolute value is positive.

`-3 - 3r = 3`

`-3r = 6`

`r = -2`

B: The absolute value is negative

`-(-3 - 3r) = 3`

`3 + 3r = 3`

`3r = 0`

`r = 0`

The solutions are `r = 0 and r = -2`. However, let's check that the solutions satisfy the original equation before stating the solution set.

`-7|-3 - 3(0)| =^? -21`

`-7|-3| =^? -21`

`-7(3) = -21`

AND

`-7|-3 - (-3 xx -2)| =^? -21`

`-7|3| =^? -21`

`-7(3) = -21`

Hence, neither of the solutions are extraneous. The solution set is `{0, -2}`.

Hopefully this helps!