Write the following inequality in interval notation.

x

Question

Write the following inequality in interval notation.

x < –2 and x ≤ 7

BlackTom AI · Accepted Answer

The task asks to write the inequality x < -2 and x ≤ 7 in interval notation.
First, examine the two conditions on x:
- x < -2 means x is strictly less than -2, so the interval on this condition is (-∞, -2).
- x ≤ 7 means x is at most 7, which corresponds to (-∞, 7].
When you combine two conditions with 'and', you need the set of x that satisfies both simultaneously. The more restrictive condition is x < -2, since all numbers less than -2 are automatically less than 7 as well. Therefore, the intersection of (-∞, -2) and (-∞, 7] is (-∞, -2).
Note that the boundary at -2 is not included, because x < -2 is strict, while any number less than -2 satisfies x ≤ 7 as well. In interval notation, this is written as (-∞, -2).
There are no additional considerations or alternative representations needed beyond recognizing the intersection of the two given inequalities.

ST-MATH-1021-771-49502-202503 Quiz 1

Write the following inequality in interval notation. x < –2 and x ≤ 7

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