Question

Solve the equation. |x+7| = 2

Answer 1

The vertical bars indicate an absolute value function.

This means that whatever comes out of it, has to be positive.

So, if the part inside is positive or zero, we can just remove the bars, but if the inside is negative, we need to change the sign of the inside part while removing the bars.

So, we have two possibilities:

`\begin{gathered} x+7\ge0\colon \\ |x+7|=2 \\ x+7=2 \\ x=2-7 \\ x=-5 \end{gathered}`

And:

`\begin{gathered} x+7<0\colon \\ |x+7|=2 \\ -(x+7)=2 \\ x+7=-2 \\ x=-2-7 \\ x=-9 \end{gathered}`

So, the soltuions are:

`\begin{gathered} x=-5 \\ x=-9 \end{gathered}`