Question 142050

{{{abs(3-6x)=15}}} Start with the given equation



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


{{{3-6x=-15}}} or {{{3-6x=15}}} Set the expression {{{3-6x}}} equal to the original value 15 and it's opposite -15





Now lets focus on the first equation  {{{3-6x=-15}}}



{{{-6x=-15-3}}}Subtract 3 from both sides



{{{-6x=-18}}} Combine like terms on the right side



{{{x=(-18)/(-6)}}} Divide both sides by -6 to isolate x




{{{x=3}}} Divide





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Now lets focus on the second equation {{{3-6x=15}}}




{{{-6x=15-3}}}Subtract 3 from both sides



{{{-6x=12}}} Combine like terms on the right side



{{{x=(12)/(-6)}}} Divide both sides by -6 to isolate x




{{{x=-2}}} Divide






So the solutions to {{{abs(3-6x)=15}}} are:


{{{x=3}}} and {{{x=-2}}}




Notice if we graph  {{{y=abs(3-6x)}}} and {{{y=15}}} (just set each side equal to y and graph), we get



{{{graph(500,500,-4,5,-5,18,abs(3-6x),15)}}}  Graph of {{{y=abs(3-6x)}}} (red) and {{{y=15}}}(green)


and we can see the two graphs intersect at {{{x=3}}} and {{{x=-2}}}. So this verifies our answer.