Solution assignment 10 Linear inequalities

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Assignment 10

Solve:

\displaystyle\frac{x+1}{x-1}>0

Solution

We draw three number lines: one for the numerator, the second one for the denominator and the third one for the quotient. The first line shows that x-1 is equal to 0 for x=+1, positive (+) for x>+1 and negative (-) for x<+1.

----------------- (+1) ++++ x-1
----- (-1) +++++++++++ x+1
+++ (-1) ----- (+1) ++++ quotiënt

From this we can determine the sign of the quotient of both linear functions because:
- / - = +
+ / + = +
+ / - = -
- / - = +

and find:

x<-1 or x>1

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