143k views
3 votes
|x+10|=4x-8 need help to figure out this answer

User Petr Marek
by
7.8k points

2 Answers

3 votes

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.

User Elo
by
8.0k points
5 votes
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
User Dnyaneshwar Harer
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories