SOLUTION: |2x-4|=12 please help me solve. Thank you!

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Question 163776: |2x-4|=12

please help me solve. Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%282x-4%29=12 Start with the given equation


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

2x-4=-12 or 2x-4=12 Set the expression 2x-4 equal to the original value 12 and it's opposite -12




Now lets focus on the first equation 2x-4=-12


2x=-12%2B4Add 4 to both sides


2x=-8 Combine like terms on the right side


x=%28-8%29%2F%282%29 Divide both sides by 2 to isolate x



x=-4 Divide






Now lets focus on the second equation 2x-4=12



2x=12%2B4Add 4 to both sides


2x=16 Combine like terms on the right side


x=%2816%29%2F%282%29 Divide both sides by 2 to isolate x



x=8 Divide





So the solutions to abs%282x-4%29=12 are:

x=-4 and x=8



Notice if we graph y=abs%282x-4%29 and y=12 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-6%2C10%2C-10%2C15%2Cabs%282x-4%29%2C12%29 Graph of y=abs%282x-4%29 (red) and y=12(green)

and we can see the two graphs intersect at x=-4 and x=8. So this verifies our answer.