Question 339198
{{{3/5+2*abs(2-(3/4)x)=7}}} Start with the given equation.



{{{2*abs(2-(3/4)x)=7-3/5}}} Subtract {{{3/5}}} from both sides.



{{{2*abs(2-(3/4)x)=32/5}}} Combine like terms.



{{{abs(2-(3/4)x)=(32/5)(1/2)}}} Multiply both sides by {{{1/2}}}



{{{abs(2-(3/4)x)=32/10}}} Multiply.



{{{abs(2-(3/4)x)=16/5}}} Reduce.



Now remember that if {{{abs(x)=a}}}, then {{{x=a}}} or {{{x=-a}}}



This means that if {{{abs(2-(3/4)x)=16/5}}}, then {{{2-(3/4)x=16/5}}} or {{{2-(3/4)x=-16/5}}}



Let's solve the first equation:



{{{2-(3/4)x=16/5}}} Start with the given equation.



{{{20(2-(3/cross(4))x)=20(16/cross(5))}}} Multiply both sides by the LCD {{{20}}} to clear any fractions.



{{{40-15x=64}}} Distribute and multiply.



{{{-15x=64-40}}} Subtract {{{40}}} from both sides.



{{{-15x=24}}} Combine like terms on the right side.



{{{x=(24)/(-15)}}} Divide both sides by {{{-15}}} to isolate {{{x}}}.



{{{x=-8/5}}} Reduce.



So one solution is {{{x=-8/5}}} 


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Now let's solve {{{2-(3/4)x=-16/5}}}



{{{2-(3/4)x=-16/5}}} Start with the given equation.



{{{20(2-(3/cross(4))x)=20(-16/cross(5))}}} Multiply both sides by the LCD {{{20}}} to clear any fractions.



{{{40-15x=-64}}} Distribute and multiply.



{{{-15x=-64-40}}} Subtract {{{40}}} from both sides.



{{{-15x=-104}}} Combine like terms on the right side.



{{{x=(-104)/(-15)}}} Divide both sides by {{{-15}}} to isolate {{{x}}}.



{{{x=104/15}}} Reduce.



So another solution is {{{x=104/15}}} 



This means that the solutions to {{{3/5+2*abs(2-(3/4)x)=7}}} are {{{x=-8/5}}} or {{{x=104/15}}} 



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