Range of values of combined Inequalities

In the above diagram, x can possess any value between -4 and +3 inclusive Hence x ≥ -2 and x ≤ + 3 or -4 ≤ x and x≤+3

These two inequalities can be combined as a single inequality. Thus, -4 ≤ x ≤ + 3

Example 3

What is the range of values of x for which 2x + 6 > 2 and x – 4 < 1 are both satisfied?
Solution
2x + 6 > 2 x – 4 < 1 2x > 2 – 6 x < 1 + 4 2x > – 6 x < 5 X > -2