Question

|x+10|=4x-8 need help to figure out this answer

Answer 1

Add 8 to both sides. Subtract x from both sides. Now you have 3x=18. Now divide 3 by 18. Your answer is x=6

Answer 2

Answer:

6 is the solution.

Don't know if you are asked for extraneous solutions or not.

Step-by-step 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.