1Cademy - Writing the Inequality $$3x - y \geq 6$$ from Its Graph

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Writing the Inequality $2x + 3y < 6$ from Its Graph

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Writing the Inequality $3x - y \geq 6$ from Its Graph

When deducing the linear inequality from a graph with the boundary line $3x - y = 6$ , one must inspect the line style and the location of the shaded region. The graph displays a solid boundary line, meaning the inequality must include an equal sign, taking the form of $\leq$ or $\geq$ . To decide which symbol is correct, test a point such as the origin $(0, 0)$ . If the origin is located in the unshaded section of the coordinate plane, substituting $x = 0$ and $y = 0$ into the expression $3x - y$ must result in a false statement. The evaluation $3(0) - 0$ gives $0$ . Because the unshaded region must yield a false statement for the correct inequality, and $0 \geq 6$ is false, the inequality describing the shaded solution region is $3x - y \geq 6$ .

Updated 2026-05-06

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OpenStax Intermediate Algebra

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