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Mastering Linear Inequalities: Guided Practice & Review

Learn to graph systems of linear inequalities in standard form through guided practice and review exercises. Understand how to find intercepts, shade solution sets, and distinguish between boundary line types. Test your understanding with practical examples.

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Mastering Linear Inequalities: Guided Practice & Review

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  1. “Where the Points Lie” Systems of Linear Inequalities

  2. Systems of InequalitiesStandard Form Guided Practice Graph 2x + 3y < 15 and 2x – 3y > 12 and shade the solution set. To review methods of graphing inequalities from standard form, graph 2x + 3y < 15 by finding the x-and y-intercepts and2x – 3y > 12 by solving the inequality for y.

  3. Systems of InequalitiesStandard Form Review Graph 2x + 3y < 15 using x- and y-intercepts. x-intercept is (x, 0) y-intercept is (0, y) 2(0) + 3y = 15 3y = 15 y = 5 (0, 5) 2x + 3(0) = 15 2x = 15 x = 7.5 (7.5, 0) Remember, the “greater than” and “less than” inequalities have dashed boundary lines.

  4. Systems of InequalitiesStandard Form Review Test a coordinate on either side of the line to see where to shade. Try (0, 0) 2(0) + 3(0) < 15 Substitute 0 + 0 < 15 Simplify 0 < 15 Simplify This is true, so shade on the side of the test point.

  5. Systems of InequalitiesStandard Form Review Graph 2x – 3y > 12 by solving the inequality for y. Test points to verify shading. (0, –4) What is the y-intercept? What is the slope? Is the boundary line dashed or solid?

  6. Systems of InequalitiesStandard Form Review Test a coordinate on either side of the line to see where to shade. Try (0, 0) 2(0) – 3(0) > 12 0 + 0 > 12 0 > 12 This is not true, so shade on the side opposite the test point.

  7. Systems of InequalitiesStandard Form Review Shade the intersection of the two solution sets.

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