Question

EXPLAIN THE ERROR A student solves the compound inequality 15< 2x + 5 < 17 and finds the solutions of the compound inequality to be all real numbers. Explain and correct the student's mistakes. Graph the actual solutions to back up your answer.

Answer 1

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.