Question 133518
{{{-4*abs(2x-3)+7 = -1 }}} Start with the given equation



{{{-4*abs(2x-3) = -8 }}} Subtract 7 from both sides



{{{abs(2x-3) = 2 }}} Divide both sides by -4. Notice how the right side is now positive. So this means that a solution exists.




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


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





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



{{{2x=-2+3}}}Add 3 to both sides



{{{2x=1}}} Combine like terms on the right side



{{{x=(1)/(2)}}} Divide both sides by 2 to isolate x




{{{x=1/2}}} Reduce





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




{{{2x=2+3}}}Add 3 to both sides



{{{2x=5}}} Combine like terms on the right side



{{{x=(5)/(2)}}} Divide both sides by 2 to isolate x




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






So the solutions are:


{{{x=1/2}}} and {{{x=5/2}}}