Question 166187


{{{12x-18>3(3x-13)}}} Start with the given inequality.



{{{12x-18>9x-39}}} Distribute.



{{{12x>9x-39+18}}} Add {{{18}}} to both sides.



{{{12x-9x>-39+18}}} Subtract {{{9x}}} from both sides.



{{{3x>-39+18}}} Combine like terms on the left side.



{{{3x>-21}}} Combine like terms on the right side.



{{{x>(-21)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}. 



{{{x>-7}}} Reduce.



----------------------------------------------------------------------


Answer:


So the answer is {{{x>-7}}} 



So the answer in interval notation is *[Tex \LARGE \left(-7,\infty\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x>-7\right\}]



Here's the graph of the solution set


{{{drawing(500,80,-17, 3,-10, 10,
number_line( 500, -17, 3),

arrow(-7,0,3,0),
arrow(-7,0.30,3,0.30),
arrow(-7,0.15,3,0.15),
arrow(-7,-0.15,3,-0.15),
arrow(-7,-0.30,3,-0.30),

circle(-7,0,0.3),
circle(-7,0,0.3),
circle(-7,0,0.3),
circle(-7,0,0.3-0.02)
)}}}