Question

The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is?

A. (-1, 6)

B. (-infinity, infinity)

C. an empty set

D. (6, -1)

The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is?

A. (-1, 6)

B. (-infinity, infinity)

C. an empty set

D. (6, -1)

Answer 1

The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 would be such that

`2x - 5 < 7 \: \: and \: \: 4x + 10 > 6 \\ 2x < 12 \: \: and \: \: 4x > - 4 \\ x < 6 \: \: and \: \: x > - 1 \\ - 1 < x < 6`
Mathematically, -1 < x < 6 can be written as (-1,6).
Hence, option A i.e. (-1,6) is the final answer.

For second question, 2x − 5 < 7 or 4x + 10 > 6
We would have x < 6 OR x > -1.
It means x could take any value either less than 6 OR greater than -1. In other words, x could take all values on number line. Hence, option B i.e. (-infinity, infinity) would be correct answer for second question.