Question 145588
{{{5x-9>2x-7}}} Start with the given inequality




{{{5x>2x-7+9}}}Add 9 to both sides



{{{5x-2x>-7+9}}} Subtract 2x from both sides



{{{3x>-7+9}}} Combine like terms on the left side



{{{3x>2}}} Combine like terms on the right side



{{{x>(2)/(3)}}} Divide both sides by 3 to isolate x 




{{{x>2/3}}} Reduce


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Answer:

So our answer is {{{x>2/3}}}  (which is approximately {{{x>0.667}}} in decimal form)





So the answer in interval notation is *[Tex \LARGE \left(\frac{2}{3},\infty\right)]



Here's the graph of the solution set


{{{drawing(500,80,-8, 12,-10, 10,
number_line( 500, -8, 12),

arrow(2/3,0,12,0),
arrow(2/3,0.30,12,0.30),
arrow(2/3,0.15,12,0.15),
arrow(2/3,-0.15,12,-0.15),
arrow(2/3,-0.30,12,-0.30),

circle(2/3,0,0.3),
circle(2/3,0,0.3),
circle(2/3,0,0.3),
circle(2/3,0,0.3-0.02)
)}}}





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{{{5(3m-(m+4))<-2(m-4) }}} Start with the given inequality



{{{15m-5(m+4)<-2(m-4) }}} Distribute





{{{15m-5m-20<-2m+8}}} Distribute



{{{10m-20<-2m+8}}} Combine like terms on the left side



{{{10m<-2m+8+20}}}Add 20 to both sides



{{{10m+2m<8+20}}} Add 2m to both sides



{{{12m<8+20}}} Combine like terms on the left side



{{{12m<28}}} Combine like terms on the right side



{{{m<(28)/(12)}}} Divide both sides by 12 to isolate m 




{{{m<7/3}}} Reduce


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

Answer:

So our answer is {{{m<7/3}}}  (which is approximately {{{m<2.333}}} in decimal form)




So the answer in interval notation is *[Tex \LARGE \left(-\infty,\frac{7}{3}\right)]





Here's the graph of the solution set


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


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




circle(7/3,0,0.3),
circle(7/3,0,0.3),
circle(7/3,0,0.3),
circle(7/3,0,0.3-0.02)
)}}}