Question

(Sorry its math not geography,,,)

Answer 1

Answer:

Problem: $4|\frac{x}{2}+3|=8$.

Solution given: $x=-2$

The other solution: $x=-10$

Explanation:

$|\frac{x}{2}+3|=2$

Means the value inside the absolute value has to be 2 or -2 since |2|=2 and |-2|=2.

So you already have $\frac{x}{2}+3=2$.

You need that $\frac{x}{2}+3=-2$.

Let's solve this equation:

$\frac{x}{2}+3=-2$

Subtract 3 on both sides:

$\frac{x}{2}=-2-3$

Simplify:

$\frac{x}{2}=-5$

Multiply both sides by 2:

$x=-5(2)$

Simplify:

$x=-10$

So x=-2 or x=-10.

Checking!

x=-2:

$4|\frac{-2}{2}+3|=8$

$4|-1+3|=8$

$4|2|=8$

$4(2)=8$

$8=8$ is true so x=-2 checks out.

x=-10:

$4|\frac{-10}{2}+3|=8$

$4|-5+3|=8$

$4|-2|=8$

$4(2)=8$

$8=8$ is true x=-10 checks out.

It has been confirmed that -2 and -10 satisfy the equation:

$4|\frac{x}{2}+3|=8$.