Question 336367


{{{abs(2x+4)=8}}} Start with the given equation



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


{{{2x+4=-8}}} or {{{2x+4=8}}} Set the expression {{{2x+4}}} equal to the original value 8 and it's opposite -8





Now lets focus on the first equation  {{{2x+4=-8}}}



{{{2x=-8-4}}}Subtract 4 from both sides



{{{2x=-12}}} Combine like terms on the right side



{{{x=(-12)/(2)}}} Divide both sides by 2 to isolate x




{{{x=-6}}} Divide





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Now lets focus on the second equation {{{2x+4=8}}}




{{{2x=8-4}}}Subtract 4 from both sides



{{{2x=4}}} Combine like terms on the right side



{{{x=(4)/(2)}}} Divide both sides by 2 to isolate x




{{{x=2}}} Divide






So the solutions to {{{abs(2x+4)=8}}} are:


{{{x=-6}}} or {{{x=2}}}



To graph these on the number line, just plot points at -6 and 2 on the number line.



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Jim