Unit 7 Lesson 3: Two-Step Equations and

InequalitiesLesson 3: Two-Step Inequalities

Cornell Notes HeaderTopic: Inequalities & Two-Step Equations (Unit 7 pg. 3)

How are two-step inequalities similar to and different from two-step equations?

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Chp. 10 Lesson 5 (6th grade my.hrw.com) – Two-Step Inequalities

Introduction ProblemMr. 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 11. 9 10 11 12 13 14

1. Solve the two-step inequality just like solving a two- step equation (follow the reverse of the order of operations).

5t + 7 ≤ 62Subtract 7 from both sides.

Divide both sides by 5. - 7 - 75t ≤ 55__ ___ 5 5t ≤ 11

ProblemMr. 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/2 - 6 > 10 + 6 + 6 Add 6 to both sides to undo subtracting 6. x/2

> 16

2 ∙ x/2 > 16 · 2 Multiply 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 > 10 11 > 10

29 30 31 32 33 34 35

SummarySummarize your notes in one to two

sentences using the words two-step inequality and graphing.