What is a compound inequality and how is it solved

Asked by admin @ 28/10/2021 in Mathematics viewed by 269 People

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.

Answered by admin @ 28/10/2021

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.

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