Answer:
6 is the solution.
Don't know if you are asked for extraneous solutions or not.
Explanation:
|x+10|=|-1(x+10)| since |1|=|-1|.
So what this tells us is we have two equations to solve:
x+10=4x-8 or -(x+10)=4x-8
Let's solve:
x+10=4x-8
Add 8 on both sides:
x+18=4x
Subtract x on both sides:
18=3x
Divide both sides by 3:
18/3=x
Simplify:
6=x
Now to solve:
-(x+10)=4x-8
Distribute:
-x-10=4x-8
Add x on both sides:
-10=5x-8
Add 8 on both sides:
-2=5x
Divide both sides by 5:
-2/5=x
You have two possible solutions:
x=6
x=-2/5
Let's check because you may wind up with an extraneous solution (one that isn't a solution to the initial equation):
Check x=6:
|x+10|=4x-8 for x=6
|6+10|=4(6)-8
|16|=24-8
16=16
You have the same thing on both sides so x=6 checks out.
Check x=-2/5:
|x+10|=4x-8 for x=-2/5
|-2/5+10|=4(-2/5)-8
|48/5|=(-8/5)-8
48/5=-48/5
You don't have the same thing on both sides so x=-2/5 doesn't check out.
So x=6 is the only solution.