Question 149693


{{{abs(5x-3)=10}}} Start with the given equation



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


{{{5x-3=-10}}} or {{{5x-3=10}}} Set the expression {{{5x-3}}} equal to the original value 10 and it's opposite -10





Now lets focus on the first equation  {{{5x-3=-10}}}



{{{5x=-10+3}}}Add 3 to both sides



{{{5x=-7}}} Combine like terms on the right side



{{{x=(-7)/(5)}}} Divide both sides by 5 to isolate x




{{{x=-7/5}}} Reduce





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Now lets focus on the second equation {{{5x-3=10}}}




{{{5x=10+3}}}Add 3 to both sides



{{{5x=13}}} Combine like terms on the right side



{{{x=(13)/(5)}}} Divide both sides by 5 to isolate x




{{{x=13/5}}} Reduce






So the solutions to {{{abs(5x-3)=10}}} are:


{{{x=-7/5}}} and {{{x=13/5}}}