Question

Explain the steps in solving the following absolute value equation. 2|x−2|=12. (There should be two answers)

Answer 1

Hello @GalacticPlunder :) Sorry for the slightly late response :-/

first we should try to get the absolute values alone on one side
so I suggest dividing both sides by 2 first :)

can you do that?

Answer 2

So it world be: x-2 = 6. Then if I add two it would be x = 8 right? My teacher said there should be two answers though. I don't know what that means :/

Answer 3

it's just saying that

for example
if |x| = 2
then if can be split up into two equations:
x = 2 and x = -2

this way:
|x - 2| = 6
can be split up into
x - 2 = 6 and x - 2 = -6

Answer 4

How can it be split into two equations?

Answer 5

the absolute value means that anything inside it comes out as a positive value

absolute value of +2 = | 2 | = 2
and
| - 2 | = 2

so if a "variable" is in the absolute value, there can be two answers (one for the positive/normal idea, and one for the negative idea)

Answer 6

ohhhh Thanks so much!

Answer 7

Could you help me with another?

Answer 8

sure thing :)

Answer 9

How do you show where an inequality is true on a number line?

Answer 10

Also this was added: "let's say you had a solution of x>2. How would you show this on a number line"

Answer 11

you would start on \(2\) :P

then if the inequality > < thing has a line under it, it would mean \(include~the~number\) and be a dark circle (not the hollow one I drew)

if the wider part of the > is facing the variable
like \(x>\) that means you should shade the numbers Bigger than the given number

Answer 12

Thanks! Could you help me with one last problem?

Answer 13

of course :)

Answer 14

What is a literal equation? How is solving a literal equation different from solving a one- or two-step equation?

Answer 15

A literal equation is an equation that is made up of all letters [variables]
for example: \(A=b*h\)

The difference between a one- or two-step equation and a literal equation is that in a one- or two-step equation, the aim (usually) is to get a numerical answer (a number as the answer). But for a literal equation, solving for a variable simply rearranges the original equation.

Sorry if that's a little confusing, here's a link about literal equations that describes it better :) http://www.purplemath.com/modules/solvelit.htm

Answer 16

Awesome! Thank you so much!

Answer 17

Glad I could help :)