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List all integers satisfying the inequality in -2 < 2x – 6 < 4 

A. 2, 3, 4 and 5

B. 2, 3

C. 2, 5

D. 3, 4

QUICK ANSWER…

D

DETAILS…

All the integers satisfying the inequality in -2 < 2x – 6 < 4 are 3, and 4.

-2 < 2x – 6 < 4 

Solving the left-hand side,

-2 < 2x – 6

-2 + 6 < 2x

4 < 2x

4/2 < 2

2 < x 

Or x > 2…………………………………………….EQ1

Now, solving the right-hand side, we have:

2x – 6 < 4

2x < 4 + 6

2x < 10

x < 10/2

x < 5   ………………………………………….EQ2

thus, combining the two sides again, we have:

2 < x < 5

So, x is greater than 2 and also less than 5.

So, the range of values for x will be from 3 to 4 which is in fact 3, and 4.

Now for the right answer to the above question:

1. Option A is not correct.
2. Option B is not correct.
3. C is incorrect.
4. D is the correct answer.

KEY-POINTS…

You may please note these/this:

• When faced with a similar question, please split it into two and solve them separately.
• 2 < x < 5 is the same as 5 > x > 2

If you love our answers, you can simply join our community and also provide answers like this, fellow learners like you will appreciate it.

/ culled from 2021 JAMB-UTME MATHEMATICS question 37 /