SOLUTION: what is a solution to 3x-6=3 with absolute value lines around the 3x-6 part

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Question 198871: what is a solution to 3x-6=3 with absolute value lines around the 3x-6 part
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%283x-6%29=3 Start with the given equation


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

3x-6=-3 or 3x-6=3 Set the expression 3x-6 equal to the original value 3 and it's opposite -3




Now lets focus on the first equation 3x-6=-3


3x=-3%2B6Add 6 to both sides


3x=3 Combine like terms on the right side


x=%283%29%2F%283%29 Divide both sides by 3 to isolate x



x=1 Divide






Now lets focus on the second equation 3x-6=3



3x=3%2B6Add 6 to both sides


3x=9 Combine like terms on the right side


x=%289%29%2F%283%29 Divide both sides by 3 to isolate x



x=3 Divide





So the solutions to abs%283x-6%29=3 are:

x=1 and x=3



Notice if we graph y=abs%283x-6%29 and y=3 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-1%2C5%2C-10%2C10%2Cabs%283x-6%29%2C3%29 Graph of y=abs%283x-6%29 (red) and y=3(green)

and we can see the two graphs intersect at x=1 and x=3. So this verifies our answer.