Practice Test

Question 5 • Algebra II

Which graph shows the solution to the inequality start absolute value x plus 3 end absolute value is greater than or equal to 2 ?

Answer

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on negative 5 and negative 1 and are connected.

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on 1 and 5 and are connected.

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on 1 and 5 and are going in the opposite direction.

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on negative 5 and negative 1 and are going in the opposite direction.

Explanation

The absolute value inequality |x + 3| ≥ 2 means x + 3 is at least 2 units from 0. So x + 3 ≥ 2 gives x ≥ −1, or x + 3 ≤ −2 gives x ≤ −5. The endpoints are included, so the graph has closed circles at −5 and −1 with rays extending outward; that is choice D.

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