Question 180763


{{{-4*abs(3x-7)=-20}}} Start with the given equation



{{{abs(3x-7)=5}}} Divide both sides by -4




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


{{{3x-7=-5}}} or {{{3x-7=5}}} Set the expression {{{3x-7}}} equal to the original value 5 and it's opposite -5





Now lets focus on the first equation  {{{3x-7=-5}}}



{{{3x=-5+7}}}Add 7 to both sides



{{{3x=2}}} Combine like terms on the right side



{{{x=(2)/(3)}}} Divide both sides by 3 to isolate x




{{{x=2/3}}} Reduce





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Now lets focus on the second equation {{{3x-7=5}}}




{{{3x=5+7}}}Add 7 to both sides



{{{3x=12}}} Combine like terms on the right side



{{{x=(12)/(3)}}} Divide both sides by 3 to isolate x




{{{x=4}}} Divide






So the solutions to {{{-4*abs(3x-7)=-20}}} are:


{{{x=2/3}}} and {{{x=4}}}