Algebra two :) please help?

Question

Which represents the compound inequality x ≥ -2 and x < 4 using interval notation?

Which represents the compound inequality x < -2 or x ≥ 3 using interval notation?

Which is the solution set of the compound inequality?
-4 < a + 2 < 10

Which is the graph of the solution set of the compound inequality?
7 ≤ x + 4 or x - 1 ≥ 5

Answer 1

 x ≥ - 2 and x < 4

Interval notation is [-2, 4)

The compound inequality is -2 ≤ x < 4

 

Answer 2

x < -2 or x ≥ 3

Compound inequality solution is intersection of two inequalities .

There is no solution of compound inequality.

Answer 3

The compound inequality is - 4 < a + 2 < 10

Solve the inequality: - 4 < a + 2

- 4 - 2 < a

- 6 < a

a > -6

Solve the inequality: a + 2 < 10

a < 10 - 2

a < 8

The solution of the compound inequality is - 6 < a < 8

Solution set is {a∈R| -6 < a < 8}

Observe the graph intersection area is solution set of the inequality and -6 and 8 are not included in the solution set.

Answer 4

The compound inequality is 7 ≤ x + 4 or x - 1 ≥ 5

Solve the inequality: 7 ≤ x + 4

7 - 4 ≤ x

3 ≤ x

x ≥ 3

Solve the inequality: x - 1 ≥ 5

x ≥ 5 + 1

x ≥ 6

The solution of the compound inequality is  x ≥ 3

Solution set is {x∈R| x ≥ 3}

Solution in interval notation [3, ∞)

Observe the graph 3 is included in the solution set.