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The solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
The interval notations are used to represent numbers between two numbers excluding or including the numbers as per the use. We use the following four interval notations:
[a, b] ⇒ All numbers between a and b including both a and b.
(a, b) ⇒ All numbers between a and b excluding both a and b.
(a, b] ⇒ All numbers between a and b excluding a but including b.
[a, b) ⇒ All numbers between a and b including a but excluding b.
We are asked to write the solution for x ≥ 0 and x ≥ -5 in the interval notation.
We first write each inequality in interval notation:
x ≥ 0 ⇒ x are all numbers greater than 0 including 0. This can be written in the interval notation as [0, ∞). We don't include ∞ as it is indeterminant.
x ≥ -5 ⇒ x are all numbers greater than -5 including -5. This can be written in the interval notation as [-5, ∞). We don't include ∞ as it is indeterminant.
Now, we are asked to solve for x ≥ 0 or x ≥ -5. Since it is 'or', we take unions of the two sets, that is the solution is:
[0, ∞) ∪ [-5, ∞) = [5, ∞).
Therefore, the solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
Learn more about the interval notation at
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