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

Question

asked Aug 10, 2023 188k views

1 Answer

Eric Galluzzo · Answer 1 · 2023-08-13T12:33:20+0000

Given:

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,

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