SOLUTION: the absolute value of 6x-8=10, then x=

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Question 143550: the absolute value of 6x-8=10, then x=
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

abs%286x-8%29=10 Start with the given equation


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

6x-8=-10 or 6x-8=10 Set the expression 6x-8 equal to the original value 10 and it's opposite -10




Now lets focus on the first equation 6x-8=-10


6x=-10%2B8Add 8 to both sides


6x=-2 Combine like terms on the right side


x=%28-2%29%2F%286%29 Divide both sides by 6 to isolate x



x=-1%2F3 Reduce






Now lets focus on the second equation 6x-8=10



6x=10%2B8Add 8 to both sides


6x=18 Combine like terms on the right side


x=%2818%29%2F%286%29 Divide both sides by 6 to isolate x



x=3 Divide





So the solutions to abs%286x-8%29=10 are:

x=-1%2F3 and x=3



Notice if we graph y=abs%286x-8%29 and y=10 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-3%2C5%2C-10%2C10%2Cabs%286x-8%29%2C10%29 Graph of y=abs%286x-8%29 (red) and y=10(green)

and we can see the two graphs intersect at x=-1%2F3 and x=3. So this verifies our answer.