SOLUTION: What is the complete solution to the equation /3-6x/=15?

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Question 142050: What is the complete solution to the equation /3-6x/=15?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%283-6x%29=15 Start with the given equation


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

3-6x=-15 or 3-6x=15 Set the expression 3-6x equal to the original value 15 and it's opposite -15




Now lets focus on the first equation 3-6x=-15


-6x=-15-3Subtract 3 from both sides


-6x=-18 Combine like terms on the right side


x=%28-18%29%2F%28-6%29 Divide both sides by -6 to isolate x



x=3 Divide






Now lets focus on the second equation 3-6x=15



-6x=15-3Subtract 3 from both sides


-6x=12 Combine like terms on the right side


x=%2812%29%2F%28-6%29 Divide both sides by -6 to isolate x



x=-2 Divide





So the solutions to abs%283-6x%29=15 are:

x=3 and x=-2



Notice if we graph y=abs%283-6x%29 and y=15 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-4%2C5%2C-5%2C18%2Cabs%283-6x%29%2C15%29 Graph of y=abs%283-6x%29 (red) and y=15(green)

and we can see the two graphs intersect at x=3 and x=-2. So this verifies our answer.