Given : Compound inequality 15< 2x + 5 < 17.
Solution: In order to solve a compound inequality , we need to isolate for a variable in the middle and get rid all numbers from the middle.
Here in the given problem, we have 2x+5 in the middle.
So, we need to get rid 5 first.
5 is added to 2x. The reverse operation of addition is subtraction.
So, we need to subtract 5 from all sides, from 15, from 2x+5 and from 17.
15-5 < 2x + 5-5 < 17 -5.
On simplifying, we get
10 < 2x < 12.
Now, we got 2x in middle. We need to get rid 2 from 2x.
2 is being multiplied with x. The reverse operation of multiplication is division.
Dividing by 2, we get
10÷2 < 2x÷2 < 12÷2
5 < x < 6
We got, x is greater than 5 and less than 6.
Therefore, final answer would not be all real numbers but real numbers between 5 and 6.
Please follow the graph on number line for it.
