Question 208109


{{{7*abs(4x-13)=35}}} Start with the given equation



{{{abs(4x-13)=5}}} Divide both sides by 7



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


{{{4x-13=-5}}} or {{{4x-13=5}}} Set the expression {{{4x-13}}} equal to the original value 5 and it's opposite -5





Now lets focus on the first equation  {{{4x-13=-5}}}



{{{4x=-5+13}}}Add 13 to both sides



{{{4x=8}}} Combine like terms on the right side



{{{x=(8)/(4)}}} Divide both sides by 4 to isolate x



{{{x=2}}} Divide


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Now lets focus on the second equation {{{4x-13=5}}}



{{{4x=5+13}}}Add 13 to both sides



{{{4x=18}}} Combine like terms on the right side



{{{x=(18)/(4)}}} Divide both sides by 4 to isolate x



{{{x=9/2}}} Reduce



So the solutions are {{{x=2}}} or {{{x=9/2}}}