Question 208122


{{{abs(3x-7)+9=4}}} Start with the given equation



{{{abs(3x-7)=-5}}} Subtract 9 from both sides.



Since the expression {{{abs(3x-7)=-5}}} 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(3x-7)=-5}}}


Also, notice if we graph {{{y=abs(3x-7)+9}}} and {{{y=4}}}(just set each side equal to y and graph), we get:


{{{graph(500,500,-10,10,-10,10,abs(3x-7)+9,4)}}} Graph of {{{y=abs(3x-7)+9}}} (red) and {{{y=4}}}(green)


and we can see that the two graphs <font size=4><b>never</b></font> intersect. So there are no solutions.