SOLUTION: Solve 2|5x − 2| + 4 = 18 for x.

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Question 644626: Solve 2|5x − 2| + 4 = 18 for x.
Answer by jim_thompson5910(35256) About Me  (Show Source):
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2%2Aabs%285x-2%29%2B4=18 Start with the given equation


2%2Aabs%285x-2%29=14 Subtract 4 from both sides.


abs%285x-2%29=7 Divide both sides by 2


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


5x-2=-7 or 5x-2=7 Set the expression 5x-2 equal to the original value 7 and it's opposite -7


Now lets focus on the first equation 5x-2=-7


5x=-7%2B2Add 2 to both sides


5x=-5 Combine like terms on the right side


x=%28-5%29%2F%285%29 Divide both sides by 5 to isolate x


x=-1 Divide


Now lets focus on the second equation 5x-2=7


5x=7%2B2Add 2 to both sides


5x=9 Combine like terms on the right side


x=%289%29%2F%285%29 Divide both sides by 5 to isolate x


x=9%2F5 Reduce


So the solutions to 2%2Aabs%285x-2%29%2B4=18 are:

x=-1 or x=9%2F5


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