Question 374763


{{{5-2x<3x-2}}} Start with the given inequality.



{{{-2x<3x-2-5}}} Subtract {{{5}}} from both sides.



{{{-2x-3x<-2-5}}} Subtract {{{3x}}} from both sides.



{{{-5x<-2-5}}} Combine like terms on the left side.



{{{-5x<-7}}} Combine like terms on the right side.



{{{x>(-7)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>7/5}}} Reduce.



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


Answer:


So the solution is {{{x>7/5}}} 



Which in decimal form is {{{x>1.4}}} 



Note: most likely, the teacher will want the answer involving the fraction.




So the answer in interval notation is *[Tex \LARGE \left(\frac{7}{5},\infty\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x>\frac{7}{5}\right\}]



Here's the graph of the solution set


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

arrow(7/5,0,17,0),
arrow(7/5,0.30,17,0.30),
arrow(7/5,0.15,17,0.15),
arrow(7/5,-0.15,17,-0.15),
arrow(7/5,-0.30,17,-0.30),

circle(7/5,0,0.3),
circle(7/5,0,0.3),
circle(7/5,0,0.3),
circle(7/5,0,0.3-0.02)
)}}}


Note: there's an open circle at {{{x=7/5}}} which means that we're exluding this value.


If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">tutoring website</a>


Jim