Question 146264

{{{abs(3x+5)+4=9}}} Start with the given equation



{{{abs(3x+5)=5}}} Subtract 4 from both sides.



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


{{{3x+5=-5}}} or {{{3x+5=5}}} Set the expression {{{3x+5}}} equal to the original value 5 and it's opposite -5





Now lets focus on the first equation  {{{3x+5=-5}}}



{{{3x=-5-5}}}Subtract 5 from both sides



{{{3x=-10}}} Combine like terms on the right side



{{{x=(-10)/(3)}}} Divide both sides by 3 to isolate x




{{{x=-10/3}}} Reduce





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Now lets focus on the second equation {{{3x+5=5}}}




{{{3x=5-5}}}Subtract 5 from both sides



{{{3x=0}}} Combine like terms on the right side



{{{x=(0)/(3)}}} Divide both sides by 3 to isolate x




{{{x=0}}} Divide






So the solutions to {{{abs(3x+5)+4=9}}} are:


{{{x=-10/3}}} and {{{x=0}}}



So you are correct.