Question

Solve for the absolute value: 2|x+2|-4=10

Answer 1

Given:

`2|x+2|-4=10`

To solve for x:

Step-by-step explanation:

On simplification we get,

`\begin{gathered} 2|x+2|=10+4 \\ 2|x+2|=14 \\ |x+2|=7 \end{gathered}`

Case (i):

Let us take,

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

Case (ii):

Let us take,

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

Thus, the values of x are 5 and -9.

Final answer:

The values of x are,

`-9\text{ }and\text{ 5}`