Question 644626
{{{2*abs(5x-2)+4=18}}} Start with the given equation



{{{2*abs(5x-2)=14}}} Subtract 4 from both sides.



{{{abs(5x-2)=7}}} Divide both sides by 2



Break up the absolute value (remember, if you have {{{abs(x)=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+2}}}Add 2 to both sides



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



{{{x=(-5)/(5)}}} Divide both sides by 5 to isolate x



{{{x=-1}}} Divide



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



{{{5x=7+2}}}Add 2 to both sides



{{{5x=9}}} Combine like terms on the right side



{{{x=(9)/(5)}}} Divide both sides by 5 to isolate x



{{{x=9/5}}} Reduce



So the solutions to {{{2*abs(5x-2)+4=18}}} are:


{{{x=-1}}} or {{{x=9/5}}}



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