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Example

Graphing x3x \geq -3, x<2.5x < 2.5, and x35x \leq -\frac{3}{5} and Writing in Interval Notation

To visualize linear inequalities and formally document their solution sets, one translates the algebraic statement into a number line graph and interval notation. In the inequality x3x \geq -3, the non-strict symbol \geq dictates that the endpoint is included, so a bracket is placed at 3-3 and the region to its right is shaded; this is written as [3,)[-3, \infty) in interval notation. For the strict inequality x<2.5x < 2.5, the endpoint is excluded, meaning an open parenthesis is placed at 2.52.5, with shading to the left toward negative infinity, represented as (,2.5)(-\infty, 2.5). Similarly, for the non-strict inequality x35x \leq -\frac{3}{5}, a bracket is drawn at the 35- \frac{3}{5} boundary and the number line is shaded to the left, which translates to the interval (,35](-\infty, -\frac{3}{5}]. The process remains consistent regardless of whether the boundary value is an integer, decimal, or fraction.

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Updated 2026-04-22

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