Question

State all values of x in the interval 2 ≤ x ≤ 8 that satisfy the following inequality:

Answer 1

3x+5 > 14

3x+5-5 > 14-5 ... subtract 5 from both sides

3x > 9

3x/3 > 9/3 .... divide both sides by 3

x > 3

So x can be any number larger than 3

We're also told that $2 \le x \le 8$ meaning x is between 2 and 8 (including both endpoints).

Overlap these two intervals, and you'll get this new compound inequality: $3 < x \le 8$ so x can be larger than 3, and smaller than 8. It cannot be equal to 3, but it can equal 8. It can equal any number between 3 and 8.

If x is a whole number, then the following values are solutions: {4, 5, 6, 7, 8} so basically anything from 3 to 8, excluding 3 but including 8.

If x is a real number, then you simply write $3 < x \le 8$

note: if x is a real number, then the answer in interval notation is (3, 8]. The curved parenthesis says "exclude this endpoint" and the square bracket means "include this endpoint".