Interval notation questions???

Question

11: Solve and write in interval notation: -7 < 4x − 3 ≤ 7

(-1, 5/2]

(-1, 1]

(-∞, ∞)

(-1, ∞)

12: Solve and write in interval notation: -4x − 2 < 6 AND 3x ≥ -6

[-2, ∞)

(-∞, ∞)

(-2, ∞)

(-∞, -2]

Answer 1

11. (-1, 5/2]

-7 &lt; 4x − 3 ≤ 7

-7 + 3 &lt; 4x ≤ 7 + 3

-4 &lt; 4x ≤ 10

-1 &lt; x ≤ 10/4 = 5/2

Therefore, (-1, 5/2] is the answer.

12. [-2, ∞)

-4x − 2 &lt; 6 AND 3x ≥ -6

-4x - 2 &lt; 6

-4x - 2 + 2 &lt; 6 + 2

-4x &lt; 8

-4x/-4 &gt; 8/-4  (Division by a negative number requires we reverse the direction of the inequality sign.)

x &gt; -2

3x ≥ -6

x ≥ -6/3

x ≥ -2

Since the interval [-2, ∞) contains the complete solution to both inequalities, then it is the answer.