Question 174181
{{{abs(x-5)=3}}} Start with the given equation



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


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





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



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



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





<hr>


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




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



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






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


{{{x=2}}} and {{{x=8}}}




Notice if we graph  {{{y=abs(x-5)}}} and {{{y=3}}} (just set each side equal to y and graph), we get



{{{drawing(500,500,-2,10,-10,10,
grid(1),
graph(500,500,-2,10,-10,10,abs(x-5),3)
)}}}  Graph of {{{y=abs(x-5)}}} (red) and {{{y=3}}}(green)


and we can see the two graphs intersect at {{{x=2}}} and {{{x=8}}}. So this verifies our answer.