anonymous
  • anonymous
Solve the inequality. Write your answer using interval notation. Please give me a second to write up the inequality
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\frac{ 2x-3 }{ x+1 }\le1\]
anonymous
  • anonymous
my first thought is to make x the subject of the formula but ik that in incorrect and ill end up with only one answer. I cannt remember the method to get two answers so id be nice if you can explain as your solve the question.
jim_thompson5910
  • jim_thompson5910
what do you get when you solve the equation below for x (2x-3)/(x+1) = 1

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anonymous
  • anonymous
i would do it like this 2x-3 = x+1 and make x the subject of the formula
anonymous
  • anonymous
and get x = 4
anonymous
  • anonymous
first solve for x
jim_thompson5910
  • jim_thompson5910
good, now what is the vertical asymptote of (2x-3)/(x+1)
anonymous
  • anonymous
vertical asymptote?
anonymous
  • anonymous
|dw:1378593652265:dw| plot 4 on this type of graph
anonymous
  • anonymous
ah kk
anonymous
  • anonymous
how does that help me now?
anonymous
  • anonymous
sorry i thought you were solving for the inequality
anonymous
  • anonymous
the answer in my book is (-1, 4)
jim_thompson5910
  • jim_thompson5910
you would use the vertical asympote and the point where the two intersect to figure out the boundaries for the intervals
jim_thompson5910
  • jim_thompson5910
asymptote*
jim_thompson5910
  • jim_thompson5910
the vertical asymptote is x = -1 since x = -1 makes the denominator x+1 equal to 0
jim_thompson5910
  • jim_thompson5910
so you'll have a number line with -1 and 4 on it you'll then test each region to see which interval satisfies the inequality
jim_thompson5910
  • jim_thompson5910
does that make sense?
anonymous
  • anonymous
how does finding the value of x when the function is undefined telling us the range of the inequality?
anonymous
  • anonymous
like if i got another question like this one just solve for x and then find the value of x when the inequality is undefined?
jim_thompson5910
  • jim_thompson5910
the best way to do it is to set up a number line like this |dw:1378591727966:dw|
jim_thompson5910
  • jim_thompson5910
then plot the points -1 and 4 |dw:1378591850398:dw|
jim_thompson5910
  • jim_thompson5910
then you simply plug in each number that represents each interval there are 3 intervals and they are marked below |dw:1378591880343:dw|
jim_thompson5910
  • jim_thompson5910
if a number from a region satisfies the inequality, then that region is part of the final answer
anonymous
  • anonymous
ok i understand :) thx alot!
jim_thompson5910
  • jim_thompson5910
you're welcome

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