Example

Graphing x>2x > 2, x1.5x \leq -1.5, and x34x \geq \frac{3}{4} and Writing in Interval Notation

The procedure for graphing linear inequalities and converting them into interval notation applies universally across different inequality types and numerical boundaries. For the strict inequality x>2x > 2, an open parenthesis is drawn at 22 to demonstrate exclusion, and the number line is shaded to the right; in interval notation, this is expressed as (2,)(2, \infty). For the non-strict inequality x1.5x \leq -1.5, a square bracket includes the 1.5-1.5 boundary point, and the shading proceeds to the left, which is noted as (,1.5](-\infty, -1.5]. Finally, for the non-strict inequality x34x \geq \frac{3}{4}, a square bracket is similarly placed at 34\frac{3}{4} with shading extending to the right, yielding the interval [34,)[\frac{3}{4}, \infty). These examples parallel the same rule sets practiced with integer, decimal, and fractional endpoints.

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Updated 2026-04-22

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