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.)
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` .