Question 357123


{{{abs(4x+1)+6=15}}} Start with the given equation



{{{abs(4x+1)=9}}} Subtract 6 from both sides.



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


{{{4x+1=-9}}} or {{{4x+1=9}}} Set the expression {{{4x+1}}} equal to the original value 9 and it's opposite -9





Now lets focus on the first equation  {{{4x+1=-9}}}



{{{4x=-9-1}}}Subtract 1 from both sides



{{{4x=-10}}} Combine like terms on the right side



{{{x=(-10)/(4)}}} Divide both sides by 4 to isolate x




{{{x=-5/2}}} Reduce





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Now lets focus on the second equation {{{4x+1=9}}}




{{{4x=9-1}}}Subtract 1 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(4x+1)+6=15}}} are:


{{{x=-5/2}}} or {{{x=2}}}



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Jim