Question 338045


{{{abs(10-4x)=2}}} Start with the given equation



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


{{{10-4x=-2}}} or {{{10-4x=2}}} Set the expression {{{10-4x}}} equal to the original value 2 and it's opposite -2





Now lets focus on the first equation  {{{10-4x=-2}}}



{{{-4x=-2-10}}}Subtract 10 from both sides



{{{-4x=-12}}} Combine like terms on the right side



{{{x=(-12)/(-4)}}} Divide both sides by -4 to isolate x




{{{x=3}}} Divide





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Now lets focus on the second equation {{{10-4x=2}}}




{{{-4x=2-10}}}Subtract 10 from both sides



{{{-4x=-8}}} Combine like terms on the right side



{{{x=(-8)/(-4)}}} Divide both sides by -4 to isolate x




{{{x=2}}} Divide






So the solutions to {{{abs(10-4x)=2}}} are:


{{{x=3}}} or {{{x=2}}}




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Jim