Question 596188


{{{abs(3-2x)=5}}} Start with the given equation



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


{{{3-2x=-5}}} or {{{3-2x=5}}} Set the expression {{{3-2x}}} equal to the original value 5 and it's opposite -5





Now lets focus on the first equation  {{{3-2x=-5}}}



{{{-2x=-5-3}}}Subtract 3 from both sides



{{{-2x=-8}}} Combine like terms on the right side



{{{x=(-8)/(-2)}}} Divide both sides by -2 to isolate x




{{{x=4}}} Divide





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Now lets focus on the second equation {{{3-2x=5}}}




{{{-2x=5-3}}}Subtract 3 from both sides



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



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




{{{x=-1}}} Divide






So the solutions to {{{abs(3-2x)=5}}} are:


{{{x=4}}} or {{{x=-1}}}



This means that the solution set is {-1,4}