Unit 7: Two-Step Equations and Inequalities Lesson 2: One-Step Inequalities

Cornell Notes Header Topic: Inequalities & Two-Step Equations (Unit 7 pg. 2) E.Q.: How are one-step equations similar and different than one-step inequalities? Name: _____________________________ Date: _____________________________ Class: _____________________________ Chp. 10 Lesson 4 (6th Grade my.hrw.com) – One-Step Inequalities

Vocabulary x x > 5 Solution inequality – A statement that two quantities are not equal. The quantities are compared using >, <, ≤, ≥, & ≠. solution of an inequality – Any value of the variable that makes the statement true. Inequalities can have more than one solution. x 5 7.5 14 x > 5 0 > 5 5 > 5 7.5 > 5 14 > 5 Solution No Yes Before showing definition, ask what is an inequality. Use what you know about prefixes and root words to come up with the meaning.

Group Word Problem Melissa made $35 dollars babysitting two children for seven hours. She needs at least $199 for a new IPOD. At a minimum, how much more money does Melissa need to buy the IPOD? Write and solve a one-step inequality. n + 35 ≥ 199 where n = money still needed

Solving & Graphing One-Step Inequalities (Use the inverse operation to undo the current operation.) 1. Solve the inequality just like solving a one- step equation. n + 35 ≥ 199 Subtract 35 from both sides. 2. Graph the solution on a number line. An open (empty) circle signals that the value is not a solution (use with < & >). An closed (solid) circle signals that the value is a solution (use with ≥ and ≤). Graph n ≥ 164. 164 is a solution to the inequality, so use a closed circle. Then draw the arrow in the direction of the numbers that are larger than 164. 162 163 164 165 166 - 35 - 35 n ≥ 164

Solving and Graphing One-Step Inequalities Example w ≤ 4 1 2 3 4 5 6 7

Solving and Graphing One-Step Inequalities Example + 3 + 3 Undo the subtraction with addition. 7 ≤ n which is n ≥ 7 4 5 6 7 8 9 10

Solving and Graphing One-Step Inequalities Example 6 · x/6 > 2 · 6 Undo the division with multiplication. x > 12 9 10 11 12 13 14 15

Solving and Graphing One-Step Inequalities Example 5p ≤ 45 Undo the multiplication with division. 5 5 p ≤ 9 6 7 8 9 10 11 12

Inequality Key Words For Solving Word Problems Symbol Example less than < x is less than 8 x < 8 greater than > x is greater than 12 x > 12 less than or equal to ≤ x is less than or equal to 2 x ≤ 2 greater than or equal to ≥ x is greater than or equal to 7 x ≥ 7 at most I need at most $15 for drinks at Sea World. x ≤ 15 at least I need at least $10 for the movie. x ≥ 10 no less than I need no less than $10 a week for lunch. x ≥ 10 no more than I need no more than $10 to get lunch at McDonalds. x ≤ 10 between < x < I need between $10 and $20 for the movie. 10 < x < 20

Summary Summarize your notes in one to two sentences using the words one-step inequality, open circle, closed circle, and graphing.