Question 252621

{{{abs(3x+4)+11=4}}} Start with the given equation



{{{abs(3x+4)=-7}}} Subtract 11 from both sides.



Since the expression {{{abs(3x+4)=-7}}} 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+4)=-7}}}


Also, notice if we graph {{{y=abs(3x+4)+11}}} and {{{y=4}}}(just set each side equal to y and graph), we get:


{{{graph(500,500,-10,10,-5,15,abs(3x+4)+11,4)}}} Graph of {{{y=abs(3x+4)+11}}} (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.