How do I solve this following inequality?
Solve the following inequality.
(Write the answer in interval notation. Simplify the answer. Use integers or fractions for any numbers in the expression.)
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To start, change the inequality sign to "`=`" .Then, make the right side zero by subtracting both sides by 2.
Simplify left side.
Then, set the numerator and denominator equal to zero. And solve for x.
`x-11=0` and `x+3=0`
The two values of x above are referred as critical numbers and it divides the number line into three intervals. In each interval, assign a test value and substitute it to the original inequality equation to be able to determine if it satisfy the condition. The interval that satisfy or result to a true condition is the solution.
For interval `xlt-3` , test value is x=-4.
`17lt=2 ` (False)
For interval `-3ltxlt11` , test value is x=0.
`-1 2/3lt=2` (True)
For interval, `xgt11` , test value is x=12
`2 1/15 lt= 2` (False)
Furthermore, substitute the critical numbers to check if they are included in the solution.
Note that in fractions, zero denominator is not allowed. So, x=-3 is not a solution.
`x=11` , `(3*11-5)/(11+3)lt=2`
`2lt=2 ` (True)
Hence, the solution set of the inequality equation `(3x-5)/(x+3)lt=2` is `-3ltxlt=11` .
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