Question 198475


{{{4*abs(3-x)+3=15}}} Start with the given equation



{{{4*abs(3-x)=12}}} Subtract 3 from both sides.



{{{abs(3-x)=3}}} Divide both sides by 4




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


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





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



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



{{{-x=-6}}} Combine like terms on the right side



{{{x=(-6)/(-1)}}} Divide both sides by -1 to isolate x




{{{x=6}}} Divide





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




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



{{{-x=0}}} Combine like terms on the right side



{{{x=(0)/(-1)}}} Divide both sides by -1 to isolate x




{{{x=0}}} Divide






So the solutions to {{{4*abs(3-x)+3=15}}} are:


{{{x=6}}} and {{{x=0}}}