6 5 Solving Linear Inequalities Lesson Objective I

6 -5 Solving Linear Inequalities Lesson Objective: I will be able to … • Graph and solve linear inequalities in two variables Language Objective: I will be able to … • Read, write, and listen about vocabulary, key concepts, and examples Holt Algebra 1

6 -5 Solving Linear Inequalities Page 24 A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution of a linear inequality is any ordered pair that makes the inequality true. Holt Algebra 1

6 -5 Solving Linear Inequalities Page 26 Example 1: Identifying Solutions of Inequalities Tell whether the ordered pair is a solution of the inequality. (– 2, 4); y < 2 x + 1 4 2(– 2) + 1 4 – 4 + 1 4 < – 3 (– 2, 4) is not a solution. Holt Algebra 1 Substitute (– 2, 4) for (x, y).

6 -5 Solving Linear Inequalities Page 26 Your Turn 1 Tell whether the ordered pair is a solution of the inequality. (4, 5); y > x + 1 y>x+1 5 4+1 5 > 5 Substitute (4, 5) for (x, y). (4, 5) is not a solution. Holt Algebra 1

6 -5 Solving Linear Inequalities Page 25 Holt Algebra 1

6 -5 Solving Linear Inequalities Page 25 Graphing Linear Inequalities Step 1 Solve the inequality for y (slopeintercept form). Step 2 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >. Shade the half-plane above the line for y > Step 3 or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer. Holt Algebra 1

6 -5 Solving Linear Inequalities Page 27 Example 2: Graphing Linear Inequalities in Two Variables Graph the solutions of the linear inequality. y 2 x – 3 Step 1 The inequality is already solved for y. Step 2 Graph the boundary line y = 2 x – 3. Use a solid line for . Step 3 The inequality is , so shade below the line. Check y 2 x – 3 0 2(0) – 3 0 – 3 Holt Algebra 1 Helpful Hint The point (0, 0) is a good test point to use if it does not lie on the boundary line.

6 -5 Solving Linear Inequalities Your Turn 2 Page 28 Graph the solutions of the linear inequality: 4 x – 3 y > 12 Step 1 Solve the inequality for y. Step 2 Graph the 4 x – 3 y > 12 boundary line y = – 4 x Use a dashed line for <. – 3 y > – 4 x + 12 y< Check y< – 6 – 6 < Holt Algebra 1 – 4 (1) – 4

6 -5 Solving Linear Inequalities Page 28 Example 3: Writing an Inequality from a Graph Write an inequality to represent the graph. y-intercept: 1; slope: Write an equation in slopeintercept form. The graph is shaded above a dashed boundary line. Replace = with > to write the inequality Holt Algebra 1

6 -5 Solving Linear Inequalities Page 29 Your Turn 3 Write an inequality to represent the graph. y-intercept: 0 slope: – 1 Write an equation in slopeintercept form. y = mx + b y = – 1 x The graph is shaded below a dashed boundary line. Replace = with < to write the inequality y < –x. Holt Algebra 1

6 -5 Solving Linear Inequalities Homework Assignment #35 • Holt 6 -5 #12, 13, 15, 19 -21, 23, 26, 63 Holt Algebra 1