Question 174185
{{{abs(2x-5)-12=-5}}} Start with the given equation



{{{abs(2x-5)=7}}} Add 12 to both sides.



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


{{{2x-5=-7}}} or {{{2x-5=7}}} Set the expression {{{2x-5}}} equal to the original value 7 and it's opposite -7





Now lets focus on the first equation  {{{2x-5=-7}}}



{{{2x=-7+5}}}Add 5 to both sides



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



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




{{{x=-1}}} Divide





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Now lets focus on the second equation {{{2x-5=7}}}




{{{2x=7+5}}}Add 5 to both sides



{{{2x=12}}} Combine like terms on the right side



{{{x=(12)/(2)}}} Divide both sides by 2 to isolate x




{{{x=6}}} Divide






So the solutions are:


{{{x=-1}}} or {{{x=6}}}




Notice if we graph  {{{y=abs(2x-5)-12}}} and {{{y=-5}}} (just set each side equal to y and graph), we get



{{{drawing(500,500,-3,8,-12,8,
grid(1),
graph(500,500,-3,8,-12,8,abs(2x-5)-12,-5)

)}}}  Graph of {{{y=abs(2x-5)-12}}} (red) and {{{y=-5}}}(green)


and we can see the two graphs intersect at {{{x=-1}}} and {{{x=6}}}. So this verifies our answer.