Solving Linear Inequalities Chapter 2

Writing and Graphing Inequalities I can write and graph linear inequalities.

Writing and Graphing Inequalities Vocabulary (page 30 in Student Journal) inequality: a mathematical sentence that uses a symbol to compare expressions that are not always equal solution set: set of all solutions to an inequality (typically inequalities will have more than 1 solution)

Writing and Graphing Inequalities Core Concepts (page 30 in Student Journal) Common inequalities include less than, less than or equal to, greater than, and greater than or equal to.

Writing and Graphing Inequalities Examples (space on page 30 in Student Journal) Write an inequality to for the scenario below. a) rides starting at $19.99 b) speed limit 35 miles per hour

Writing and Graphing Inequalities Solutions a) r greater than or equal to 19.99 b) s less than or equal to 35

Writing and Graphing Inequalities Examples Determine if the following are solutions to the inequality 13 - 7y < 6. c) 0 d) 2

Writing and Graphing Inequalities Solutions c) no, 13 is not less than 6 d) yes, -1 is less than 6

Writing and Graphing Inequalities Examples e) Graph -4 > y f) Write the inequality for the graph.

Writing and Graphing Inequalities Solutions a) b) x < 12

Solving Inequalities Using Addition or Subtraction I can solve inequalities using addition and subtraction.

Solving Inequalities Using Addition or Subtraction Core Concepts (pages 35 and 36 in Student Journal) Addition Property of Inequality (a, b and c are real numbers) If a > b, then a + c > b + c If a < b, then a + c < b + c

Solving Inequalities Using Addition or Subtraction Subtraction Property of Inequality (a, b and c are real numbers) If a > b, then a - c > b - c If a < b, then a - c < b - c

Solving Inequalities Using Addition or Subtraction Examples (space on pages 35 and 36 in Student Journal) a) Solve n - 5 < -3. b) Solve -1 > y + 12.

Solving Inequalities Using Addition or Subtraction Solutions a) n < 2 b) -13 > y or y < -13

Solving Inequalities Using Multiplication or Division I can solve inequalities by multiplying or dividing.

Solving Inequalities Using Multiplication or Division Core Concepts (page 40 in Student Journal) Multiplication Property of Inequality (a, b and c are real numbers) If a > b and c > 0, then ac > bc If a < b and c > 0, then ac < bc If a > b and c < 0, then ac < bc If a < b and c < 0, then ac > bc

Solving Inequalities Using Multiplication or Division Division Property of Inequality (a, b and c are real numbers) If a > b and c > 0, then a/c > b/c If a < b and c > 0, then a/c < b/c If a > b and c < 0, then a/c < b/c If a < b and c < 0, then a/c > b/c

Solving Inequalities Using Multiplication or Division Examples (space on page 40 in Student Journal) a) what are the solutions to c/8 > ¼ ? b) what are the solutions to x/-5 < -3

Solving Inequalities Using Multiplication or Division Solutions a) c > 2 b) x > 15

Solving Inequalities Using Multiplication or Division Examples c) what are the solutions to 12a < 6 ? d) what are the solutions to -5y > -10

Solving Inequalities Using Multiplication or Division Solutions c) a < ½ d) y < 2

Solving Multi-Step Inequalities I can solve multi-step inequalities.

Solving Multi-Step Inequalities Examples (space on page 45 in Student Journal) Solve the following inequalities. a) -6a - 7 < 17 b) 15 > 5 - 2(4m + 7) c) 3b + 12 > 27 - 2b

Solving Multi-Step Inequalities Solutions a) a > 4 b) -3 < m or m > -3 c) b > 3

Solving Compound Inequalities I can write, graph, and solve compound inequalities.

Solving Compound Inequalities Vocabulary (page 50 in Student Journal) compound inequality: 2 distinct inequalities joined by the word and or the word or In order to solve a compound inequality we can take the compound inequality and separate into 2 inequalities and solve them each individually.

Solving Compound Inequalities Examples (space on page 50 in Student Journal) Write a compound inequality. a) all real numbers greater than 4 and less than 6 b) all real numbers less than 7 or greater than 12

Solving Compound Inequalities Solutions 4 < x < 6 x < 7 or x > 12

Solving Compound Inequalities Examples Solve the following inequality. c) -2 < 3y - 4 < 14

Solving Compound Inequalities Solutions c) ⅔ < y < 6

Solving Absolute Value Inequalities I can solve absolute value inequalities.

Solving Absolute Value Inequalities Core Concepts (page 55 in Student Journal) In order to solve an absolute value inequality in the form abs(A) < b, where A is a variable expression and b > 0 we can solve the compound inequality -b < A < b. If the inequality is in the form abs(A) > b we would have to solve the compound inequality A < -b or A > b.

Solving Absolute Value Inequalities Examples (space on page 55 in Student Journal) Solve the following inequalities. a) abs(2x + 4) > 5 b) abs(w - 213) < 7

Solving Absolute Value Inequalities Solutions a) x > .5 or x < -4.5 b) 206 < w < 220