Lesson 3: Two-Step Inequalities

Cornell Notes Header Topic: Inequalities & Two-Step Equations (Unit 7 pg. 3) How are two-step inequalities similar to and different from two- step equations? Name: _____________________________ Date: _____________________________ Class: _____________________________ Chp. 10 Lesson 5 (6 th grade my.hrw.com) – Two-Step Inequalities

Introduction Problem Mr. Smith wants to take his family, a wife and three children, to the movies. He has at most $62. Seven dollars will be spent buying the family a snack for the movie, and the rest will be spent on movie tickets. What amount can Mr. Smith pay for a movie ticket?

Solving & Graphing Two-Step Inequalities 2. Graph the solution on a number line. An open (empty) circle signals that the value is not a solution (use with ). A closed (solid) circle signals that the value is a solution (use with ≥ and ≤). Graph t ≤ 11. Eleven is a solution to the inequality, so use a closed circle. Then draw the arrow in the direction of the numbers that are less than Solve the two-step inequality just like solving a two- step equation (follow the reverse of the order of operations). 5t + 7 ≤ 62 Subtract 7 from both sides. Divide both sides by t ≤ 55 __ ___ 5 5 t ≤ 11

Problem Mr. Smith wants to take his family, a wife and three children, to the movies. He has at most $62. Seven dollars will be spent buying the family a snack for the movie, and the rest will be spent on movie tickets. What amount can Mr. Smith pay for a movie ticket? t ≤ 11 Mr. Smith can pay no more than $11 dollars per ticket. Can Mr. Smith take the family to the movies? We cannot determine the answer with the information given.

Solving and Graphing Two-Step Inequalities Group Problem x / > Add 6 to both sides to undo subtracting 6. x / 2 > 16 2 ∙ x / 2 > 16 · 2Multiply both sides by 2 to undo dividing by 2. x > 32 Check: 34 / 2 – 6 > 10 Choose a value larger than 32 to check. 17 – 6 > >

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