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Interval Notation and Inequalities

Interval Notation and Inequalities. Math 021. Interval Notation is a way to write a set of real numbers. The following are examples of how sets of numbers can be written in interval notation:. Solving Linear Inequalities

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Interval Notation and Inequalities

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  1. Interval Notation and Inequalities Math 021

  2. Interval Notation is a way to write a set of real numbers. The following are examples of how sets of numbers can be written in interval notation:

  3. Solving Linear Inequalities • Solving linear inequalities is similar to solving linear equations. Replace the inequality with an equal sign and solve using the same rules as solving linear equations. When solving, there is a rule of inequalities that must be followed: • If a ,b, and c are real numbers and c < 0: If a < b, then ac > bc If a > b, then ac < bc • In other words multiplying or dividing an inequality by a negative number flips the inequality.

  4. Examples – Solve, graph, and write each inequality in interval notation: • a. 3x – 1 < 11 • b. 2(x + 3) ≥ x + 4 • c. 4(3x – 1) ≤ 10(x + 1) • d. 4x + 15 + x > 3 + 2x + 6 • e. -6x - 2 ≤ 10 • f. 30 < -5x

  5. Solving Compound Inequalities • A compound inequality is any inequality that contains two or more inequality symbols. • A union between two inequalities is all the set of all elements that belongs to either inequality. • Keyword for union is Or • An intersection of two inequalities is the set of all elements that belong to both inequalities. • Keyword for intersection is And

  6. Examples – Solve, graph, and write each inequality in interval notation: • a. 6 < 3x ≤ 15 b. -6 ≤ 5x – 1 < 9 c. x + 3 d. e. f.

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