Question 146868


{{{abs(2x+6)-4=20}}} Start with the given equation



{{{abs(2x+6)=24}}} Add 4 to both sides.



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


{{{2x+6=-24}}} or {{{2x+6=24}}} Set the expression {{{2x+6}}} equal to the original value 24 and it's opposite -24





Now lets focus on the first equation  {{{2x+6=-24}}}



{{{2x=-24-6}}}Subtract 6 from both sides



{{{2x=-30}}} Combine like terms on the right side



{{{x=(-30)/(2)}}} Divide both sides by 2 to isolate x




{{{x=-15}}} Divide





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Now lets focus on the second equation {{{2x+6=24}}}




{{{2x=24-6}}}Subtract 6 from both sides



{{{2x=18}}} Combine like terms on the right side



{{{x=(18)/(2)}}} Divide both sides by 2 to isolate x




{{{x=9}}} Divide






So the solutions to {{{abs(2x+6)-4=20}}} are:


{{{x=-15}}} and {{{x=9}}}




Notice if we graph  {{{y=abs(2x+6)-4}}} and {{{y=20}}} (just set each side equal to y and graph), we get



{{{graph(500,500,-17,11,-3,21,abs(2x+6)-4,20)}}}  Graph of {{{y=abs(2x+6)-4}}} (red) and {{{y=20}}}(green)


and we can see the two graphs intersect at {{{x=-15}}} and {{{x=9}}}. So this verifies our answer.