Answer:
Problem: [tex]4|\frac{x}{2}+3|=8[/tex].
Solution given: [tex]x=-2[/tex]
The other solution: [tex]x=-10[/tex]
Explanation:
[tex]|\frac{x}{2}+3|=2[/tex]
Means the value inside the absolute value has to be 2 or -2 since |2|=2 and |-2|=2.
So you already have [tex]\frac{x}{2}+3=2[/tex].
You need that [tex]\frac{x}{2}+3=-2[/tex].
Let's solve this equation:
[tex]\frac{x}{2}+3=-2[/tex]
Subtract 3 on both sides:
[tex]\frac{x}{2}=-2-3[/tex]
Simplify:
[tex]\frac{x}{2}=-5[/tex]
Multiply both sides by 2:
[tex]x=-5(2)[/tex]
Simplify:
[tex]x=-10[/tex]
So x=-2 or x=-10.
Checking!
x=-2:
[tex]4|\frac{-2}{2}+3|=8[/tex]
[tex]4|-1+3|=8[/tex]
[tex]4|2|=8[/tex]
[tex]4(2)=8[/tex]
[tex]8=8[/tex] is true so x=-2 checks out.
x=-10:
[tex]4|\frac{-10}{2}+3|=8[/tex]
[tex]4|-5+3|=8[/tex]
[tex]4|-2|=8[/tex]
[tex]4(2)=8[/tex]
[tex]8=8[/tex] is true x=-10 checks out.
It has been confirmed that -2 and -10 satisfy the equation:
[tex]4|\frac{x}{2}+3|=8[/tex].
