3 Preview of Grade 7 AF Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations, or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).CaliforniaStandards
4 Vocabulary inequality algebraic inequality solution set compound inequality
5 Symbol Meaning Word Phrases An inequality is a statement that compares two expressions by using one of the following symbols: <, >, ≤, ≥, or .SymbolMeaningWord Phrases<>≤≥is less thanFewer than, belowis greater thanMore than, aboveis less than or equal toAt most, no more thanis greater than or equal toAt least, no less than
6 An inequality that contains a variable is an algebraic inequality An inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality.An inequality may have more than one solution. Together, all of the solutions are called the solution set.You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle.
7 x is either greater than 3 or less than–1. A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related.x > 3 or x < –1–2 < y and y < 4x is either greater than 3 or less than–1.y is both greater than –2 and less than y is between –2 and 4.The compound inequality –2 < y and y < 4 can be written as –2 < y < 4.Writing Math
8 a > 5 b ≤ 3 This open circle shows that 5 is not a solution. If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle.This closed circle shows that 3 is a solution.b ≤ 3
9 Additional Example 1: Writing Inequalities Write an inequality for each situation.A. There are at least 15 people in the waiting room.“At least” means greaterthan or equal to.number of people ≥ 15B. The tram attendant will allow no morethan 60 people on the tram.“No more than” meansless than or equal to.number of people ≤ 60
10 Additional Example 2: Graphing Simple Inequalities Graph each inequality.Draw an open circle at 3. The solutions are values of n less than 3, so shade to the left of 3.A. n < 3–3 –2 –B. a ≥ –4Draw a closed circleat –4. The solutions are –4 and values of a greater than –4, so shade to the right of –4.–6 –4 –
11 Additional Example 3: Graphing Compound Inequalities Graph each compound inequality.A. m ≤ –2 or m > 1Graph m ≤ –2Graph m > 1•246–246–2–4–6Include the solutions shown by either graph.123456–
12 Check It Out! Example 1Write an inequality for each situation.A. There are at most 10 gallons of gas in the tank.“At most” means lessthan or equal to.gallons of gas ≤ 10B. There is at least 10 yards of fabric left.“At least” meansgreater than or equal to.yards of fabric ≥ 10
13 Check It Out! Example 2 Graph each inequality. Draw a closed circle at 2. The solutions are 2 and values of p less than 2, so shade to the left of 2.A. p ≤ 2–3 –2 –B. e > –2Draw an open circleat –2. The solutions are values of e greater than –2, so shade to the right of –2.–3 –2 –
14 Lesson Quiz: Part IWrite an inequality for each situation.1. No more than 220 people are in the theater.2. There are at least a dozen eggs left.3. Fewer than 14 people attended the meeting.people in the theater ≤ 220number of eggs ≥ 12people attending the meeting < 14
15 º º Lesson Quiz: Part II Graph the inequalities. 4. x > –1 1352–Graph the compound inequality.5. x ≥ 4 or x < –1135–•
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