Question 211558
a)


{{{3*abs(x)+12=7}}} Start with the given equation



{{{3*abs(x)=-5}}} Subtract 12 from both sides.



{{{abs(x)=-5/3}}} Divide both sides by 3




Since the expression {{{abs(x)=-5/3}}} is <font size=4><b>never</b></font> true (note: remember, the absolute value of any number is <font size=4><b>always positive</b></font>), there are no solutions to {{{abs(x)=-5/3}}}



So there are no solutions.



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b)



{{{5*abs(x+3)+6=3}}} Start with the given equation



{{{5*abs(x+3)=-3}}} Subtract 6 from both sides.



{{{abs(x+3)=-3/5}}} Divide both sides by 5




Since the expression {{{abs(x+3)=-0.6}}} is <font size=4><b>never</b></font> true (note: remember, the absolute value of any number is <font size=4><b>always positive</b></font>), there are no solutions to {{{abs(x+3)=-0.6}}}



So there are no solutions.


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c) 


{{{12-abs(2x+7)>=14}}} Start with the given inequality.



{{{-abs(2x+7)>=14-12}}} Subtract 12 from both sides.



{{{-abs(2x+7)>=2}}} Combine like terms.



{{{abs(2x+7)<=-2}}} Multiply both sides by -1 (this will flip the inequality).



Because {{{abs(2x+7)>=0}}} for ALL 'x', this means that {{{abs(2x+7)<=-2}}} is simply not possible.


So there are no solutions.




So this might explain why you couldn't come up with a solution....as there are none. However, make sure that you copied down the problems correctly.