Question 163779


{{{abs(3x-5)=22}}} Start with the given equation



Break up the absolute value (remember, if you have {{{abs(x)=a}}}, then {{{x=-a}}} or {{{x=a}}})


{{{3x-5=-22}}} or {{{3x-5=22}}} Set the expression {{{3x-5}}} equal to the original value 22 and it's opposite -22





Now lets focus on the first equation  {{{3x-5=-22}}}



{{{3x=-22+5}}}Add 5 to both sides



{{{3x=-17}}} Combine like terms on the right side



{{{x=(-17)/(3)}}} Divide both sides by 3 to isolate x




{{{x=-17/3}}} Reduce





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Now lets focus on the second equation {{{3x-5=22}}}




{{{3x=22+5}}}Add 5 to both sides



{{{3x=27}}} Combine like terms on the right side



{{{x=(27)/(3)}}} Divide both sides by 3 to isolate x




{{{x=9}}} Divide






So the solutions to {{{abs(3x-5)=22}}} are:


{{{x=-17/3}}} and {{{x=9}}}