Question

What is the solutions to the equation |2x - 14| - 12 = -12?
I really need help! :/

Answer 1

First isolate the stuff in the absolute value lines on one side of the equation. What do you have at that point?

Answer 2

That is, add 12 to both sides. Now what do you have?

Answer 3

Well first isolate the absolute value
|2x - 14| = 0

now an absolute value is the distance from 0. You will now have 2 equations.

2x + 14 = 0 and 2x - 14 = 0

Now solve. you will get 2 answers for x

Answer 4

add 12 to both sides of what?

Answer 5

That's not quite right, Ryan.
Just 2x - 14 = 0. Solve that to get your only answer.

Answer 6

\(\bf |2x - 14| - 12 = -12\implies|2x - 14| = 0\\ \quad \\
|2x - 14| = 0\implies
\begin{cases}
+(2x - 14) = 0\\ \quad \\
\bf -(2x - 14) = 0
\end{cases}\)

Answer 7

a bit redundant, but anyhow

Answer 8

Sorry.. should have said you can just get rid of the abs value sign if the other side is EQUAL to 0.

Answer 9

\(\bf |2x - 14| = 0\implies
\begin{cases}
+(2x - 14) = 0\implies 2x-14 = 0\\ \quad \\

\bf -(2x - 14) = 0\implies 2x-14 = 0
\end{cases}\)

Answer 10

..so the answer would be 0? i'm sorry i'm just really lost now? you're all saying sort of different things..

Answer 11

Normally you get 2 different solutions on these linear abs value problems...unless it is 0 on the other side..then you only get one. If that number on the right were negative you would have no solution, since an absolute value can't be negative.

Answer 12

No. just solve 2x - 14 = 0 and you're done.

Answer 13

solve for "x", and you'd get your answer(s) :)

Answer 14

x = -5 or x = 2??

Answer 15

2x - 14 = 0
2x = 14
x = 7
That's you one and only answer. Plug it back into the original and you will see that it works.

Answer 16

Again.
Isolate the abs value on one side.
If the other side is positive, set the stuff in the abs value equal to the positive other side and negative other side setting up 2 equations.
If the other side is 0, just drop the abs value sign.
If the other side is negative, the ans is no solution.

Answer 17

oh! okay wow thank you! I see what I was doing wrong! thank you so much again! :)

Answer 18

No problem. Good luck.

Answer 19

I just went over this in math class like a week ago, i believe you recieve two answers because, for example: |-7| = |7|