Alan G. answered • 03/09/16
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You must solve each inequality for x and write the answer in correct interval notation.
2x - 5 ≤ -11 ⇒ 2x ≤ -6 ⇒ x ≤ -3
In interval notation, this is (-∞, -3].
5x + 1 ≥ 6 ⇒ 5x ≥ 5 ⇒ x ≥ 1
In interval notation, this is [1, ∞).
When you ask to find the interval for the compound inequality with the word "or" between them, this means you must find the union of the two intervals. This is written by placing the symbol ∪ between the two intervals. It usually best to but the interval with the smaller numbers to the left of the interval with the larger numbers.
So ... the answer is:
(-∞, -3] ∪ [1, ∞).
