Question 167745
{{{3+abs(4t-1)=8}}} Start with the given equation



{{{abs(4t-1)=5}}} Subtract 3 from both sides.



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


{{{4t-1=-5}}} or {{{4t-1=5}}} Set the expression {{{4t-1}}} equal to the original value 5 and it's opposite -5





Now lets focus on the first equation  {{{4t-1=-5}}}



{{{4t=-5+1}}}Add 1 to both sides



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



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




{{{t=-1}}} Divide





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Now lets focus on the second equation {{{4t-1=5}}}




{{{4t=5+1}}}Add 1 to both sides



{{{4t=6}}} Combine like terms on the right side



{{{t=(6)/(4)}}} Divide both sides by 4 to isolate t




{{{t=3/2}}} Reduce





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Answer:



So the solutions are:


{{{x=-1}}} and {{{x=3/2}}}