Question 146866


{{{abs(3x+2)=14}}} Start with the given equation



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


{{{3x+2=-14}}} or {{{3x+2=14}}} Set the expression {{{3x+2}}} equal to the original value 14 and it's opposite -14





Now lets focus on the first equation  {{{3x+2=-14}}}



{{{3x=-14-2}}}Subtract 2 from both sides



{{{3x=-16}}} Combine like terms on the right side



{{{x=(-16)/(3)}}} Divide both sides by 3 to isolate x




{{{x=-16/3}}} Reduce





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Now lets focus on the second equation {{{3x+2=14}}}




{{{3x=14-2}}}Subtract 2 from both sides



{{{3x=12}}} Combine like terms on the right side



{{{x=(12)/(3)}}} Divide both sides by 3 to isolate x




{{{x=4}}} Divide






So the solutions to {{{abs(3x+2)=14}}} are:


{{{x=-16/3}}} and {{{x=4}}}