Question 174312

{{{abs(x-6)=4}}} Start with the given equation



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


{{{x-6=-4}}} or {{{x-6=4}}} Set the expression {{{x-6}}} equal to the original value 4 and it's opposite -4





Now lets focus on the first equation  {{{x-6=-4}}}



{{{x=-4+6}}}Add 6 to both sides



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





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Now lets focus on the second equation {{{x-6=4}}}




{{{x=4+6}}}Add 6 to both sides



{{{x=10}}} Combine like terms on the right side





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Answer:



So the solutions are:


{{{x=2}}} or {{{x=10}}}




Notice if we graph  {{{y=abs(x-6)}}} and {{{y=4}}} (just set each side equal to y and graph), we get



{{{drawing(500,500,-3,12,-10,10,
grid(1),
graph(500,500,-3,12,-10,10,abs(x-6),4)
)}}}  Graph of {{{y=abs(x-6)}}} (red) and {{{y=4}}}(green)


and we can see the two graphs intersect at {{{x=2}}} and {{{x=10}}}. So this verifies our answer.