Question 198054
{{{abs(2x-7)=12}}} Start with the given equation



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


{{{2x-7=-12}}} or {{{2x-7=12}}} Set the expression {{{2x-7}}} equal to the original value 12 and it's opposite -12





Now lets focus on the first equation  {{{2x-7=-12}}}



{{{2x=-12+7}}}Add 7 to both sides



{{{2x=-5}}} Combine like terms on the right side



{{{x=-5/2}}} Reduce



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Now lets focus on the second equation {{{2x-7=12}}}




{{{2x=12+7}}}Add 7 to both sides



{{{2x=19}}} Combine like terms on the right side



{{{x=(19)/(2)}}} Divide both sides by 2 to isolate x




{{{x=19/2}}} Reduce






So the solutions to {{{abs(2x-7)=12}}} are:


{{{x=-5/2}}} and {{{x=19/2}}}