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Multiply by Tens - Lesson 3.1

Estimate Products - Lesson 3.2

Area Models and Partial Products - Lesson 3.3

Multiply Using Partial Products - Lesson 3.4

Multiply with Regrouping - Lesson 3.5

Choose a Multiplication Method - Lesson 3.6  

Problem Solving - Multiply 2-Digit Numbers - Lesson 3.7

Multiplication Comparing Using Algebra - Lesson 2.1

Comparison Problems - Section 2.2

Multiply Tens, Hundreds & Thousands - Lesson 2.3

Estimate Products - Lesson 2.4

Multiply with the Distributive Property - Lesson 2.5

Multiply Using Expanded Form - Lesson 2.6

Multiply Using Partial Products - Lesson 2.7

Multiply Using Mental Math - Lesson 2.8

Problem Solving With Multistep Multiplication - Lesson 2.9

Multiply 2-Digit Numbers With Regrouping - Lesson 2.10

Multiply 3 and 4-Digit Numbers With Regrouping - Lesson 2.11

Solve Multistep Problems Using Equations - Lesson 2.12

Lines, Rays, and Angles - Lesson 10.1

Classify Triangles - Lesson 10.2

Parallel and Perpendicular Lines - Lesson 10.3

Classify Quadrilaterals - Lesson 10.4

Line symmetry - lesson 10.5, find and draw lines of symmetry - lesson 10.6, problem solving: shape patterns - lesson 10.7   , relate tenths and decimals - lesson 9.1.

Relate Hundredths and Decimals - Lesson 9.2  

Equivalent Fractions and Decimals - Lesson 9.3

Relate Fractions, Decimals, and Money - Lesson 9.4

Problem Solving With Money - Lesson 9.5

Add Fractional Parts of 10 and 100 - Lesson 9.6

Compare Decimals - Lesson 9.7

Add & Subtract Parts of a Whole - Section 7.1

Write Fractions as Sums - Section 7.2

Adding Fractions Using Models - Section 7.3

Subtract Fractions Using Models - Section 7.4

Add and Subtract Fractions - Section 7.5

Rename Fractions and Mixed Numbers - Section 7.6

Add & Subtract Mixed Numbers - Section 7.7

Subtraction with Renaming - Section 7.8

Fractions and Properties of Addition - Section 7.9

Problem Solving Using Multistep Fractions - Section 7.10

Chapter 7 Test Review on Add and Subtract Fractions

Equivalent Fractions - Section 6.1

Gener ate Equivalent Fractions - Section 6.2

Fractions in Simplest Form - Section 6.3

Common Denominators - Section 6.4

Problem Solving With Equivalent Fractions - Section 6.5  

Compare Fractions - Section 6.6

More Comparing Fractions - Section 6.7

Compare and Order Fractions - Section 6.8

Chapter 6 Review on Fraction Equivalence and Comparison

Modeling Factors of Numbers - Section 5.1

Factors and Divisibility - Section 5.2  

Problem Solving With Common Factors - Section 5.3

Factors and Multiples - Section 5.4

Prime and Composite Numbers - Section 5.5

Number Patterns - Lesson 5.6

Review For Test on Chapter 5; Factors, Multiples, and Patterns

Estimate Quotients Using Multiples - Lesson 4.1

Remainders - Lesson 4.2

Interpret the Remainder - Lesson 4.3

Divide Tens, Hundreds, and Thousands - Lesson 4.4

Estimate Quotients Using Compatible Numbers - Lesson 4.5

Division and the Distributive Property - Lesson 4.6

Divide Using Repeated Subtraction - Lesson 4.7

Divide 3 Digits by 1 Using Partial Quotients - Section 4.8

Divide 3 Digits by 1 With Regrouping - Section 4.9

Divide 3 Digits by 1 Using Place Value - Section 4.10

Divide By 1 Digit Numbers Using Place Value - Section 4.11

Multi-Step Problem Solving with Whole Numbers-Section 4.12

Fourth Grade

• AP Calculus
• AP Statistics
• Independent Study
• Second Grade Math
• Third Grade Math
• Fourth Grade Math
• Fifth Grade Math
• Sixth Grade Math
• Sixth Grade Math (CA)
• Seventh Grade Math (CA)
• Eighth Grade Math (CA)
• Integrated Math 1
• Integrated Math 2
• Integrated Math 3
• PreCalculus
• AP Statistics Exam Prep
• Elementary Statistics
• ELM Practice
• Percents and Decimals
• Sixth Grade Math (Big Ideas)

Perimeter - Lesson 13.1

Area - Lesson 13.2

Area of Combined Rectangles - Lesson 13.3

Find Unknown Measures - Lesson 13.4

Problem Solving - Find the Area - Lesson 13.5

Angles and Fractional Parts of a Circle - Lesson 11.1

Degrees - Lesson 11.2

Measure and Draw Angles - Lesson 11.3

Joint and Separate Angles - Lesson 11.4

Problem Solving: Unknown Angle Measures - Lesson 11.5

Measurement Benchmarks - Lesson 12.1

Customary Units of Length - Lesson 12.2

Customary Units of Weight - Lesson 12.3

Customary Units of Liquid Volume - Lesson 12.4

Line Plots - Lesson 12.5

Show What You Know (Pre-Chapter 1)

Vocabularly Builder (Pre-Chapter 1)

Model Place Value Relationship - Lesson 1.1

Read and Write Numbers - Lesson 1.2

  Compare and Order Numbers - Lesson 1. 3  

Rounding Numbers - Lesson 1.4

Renaming Numbers - Lesson 1.5

Adding Whole Numbers - Lesson 1.6

Subtracting Whole Numbers - Lesson 1.7

Problem Solving - Lesson 1.8

Multiples of Unit Fractions - Lesson 8.1

Multiples of Fractions - Lesson 8.2

Multiply Fractions by Whole Numbers - Lesson 8.3  

Multiply Fractions and Mixed Numbers by Whole Numbers 8 4

Comparison Problem Solving with Fractions - Lesson 8.5

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Curriculum  /  Math  /  7th Grade  /  Unit 4: Equations and Inequalities  /  Lesson 10

Equations and Inequalities

Lesson 10 of 12

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Solve inequalities with negative coefficients.

Common Core Standards

Core standards.

The core standards covered in this lesson

Expressions and Equations

7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Foundational Standards

The foundational standards covered in this lesson

6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.EE.B.8 — Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Understand that solving a corresponding equation to an inequality will give the value for the variable where the solutions begin; testing solutions on either side of this value will indicate the direction of the solutions to the inequality.
• Understand that in solving an inequality with a negative coefficient, the variable term can be added to both sides and solved with a positive coefficient; in this case the relationship of the variable to the inequality symbol has flipped. For example, the solution to  $$-2x<6 $$  is not values for $$x$$  that are less than $$-3$$ , but rather values for $$x$$  that are greater than $$-3$$ .
• Solve inequalities with negative coefficients. 

Suggestions for teachers to help them teach this lesson

• In Lesson 10, students encounter inequalities with negative coefficients and must make sense of an unexpected solution. The three Anchor Problems guide students through different approaches to understanding these problems conceptually rather than as a trick of “flipping the inequality symbol.”
• A common misconception that happens if students learn only the rule and not the conceptual understanding behind it is to over-apply the rule whenever there is a negative in the problem. For example, a student who does not understand this concept may solve  $${3x>-9}$$ and $${-3x>9}$$ the same way as $${x <-3.}$$  If the student were to test out possible values for the solution into the inequality, the student would see that this is the solution to only one of those inequalities. 

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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

In the chart below, one equation and three inequalities are shown. For each one, write the solution and use the space in the last row to check your solution. 

What challenges arise with the inequality $${-3x<12}$$ ? Is this what you expected to happen?

Guiding Questions

Ralph is trying to solve the inequality $${-{ 1\over 3}(x-48)\leq15.}$$  He knows how to solve equations, so he writes the corresponding equation $${-{ 1\over 3}(x-48)=15.}$$

a.   Solve Ralph’s equation and plot the point on the number line below. How is the solution to the equation related to the solution to the inequality?

b.   Pick a number either to the right or to the left of the point you drew on the number line. Test this number as a solution to the inequality. What does this tell you about the direction of the solutions to the inequality?

c.   Write the solution to the inequality using an inequality symbol.

Rakiah is solving the inequality - $${2x+5>1.}$$ She is unsure how to treat the negative 2 in the inequality, so she uses the addition property of equality to rewrite her inequality. See her work below.

Is Rakiah’s solution correct? Justify your answer.

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Match each inequality to one of the solutions. Justify that your solution is correctly matched to your inequality. 

Inequalities:

$${-10-6x>26}$$             $${-10+6x>-46}$$

$${x>-6 }$$           $${x>6}$$           $${ x<-6}$$             $${x<6}$$

Student Response

An example response to the Target Task at the level of detail expected of the students.

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• Open Middle Creating Inequalities — Challenge
• Kuta Software Free Algebra 1 Worksheets One-Step Inequalities
• Kuta Software Free Pre-Algebra Worksheets Two-Step Inequalities
• Open Up Resources Grade 7 Unit 6 Practice Problems — Lessons 14 and 15
• Algebra By Example 5.2 Multiplying and Dividing Inequalities

Topic A: Solving and Modeling with Equations

Solve one-step equations with rational numbers.

Represent equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ using tape diagrams.

Solve equations in the forms $${px+q=r}$$   and $${p(x+q)=r}$$  using tape diagrams.

7.EE.B.3 7.EE.B.4.A

Solve equations in the forms $${px+q=r }$$  and $${p(x+q)=r}$$  algebraically.

Solve word problems leading to equations in the forms $${px+q=r}$$   and $${p(x+q)=r}$$ (Part 1).

Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r }$$  (Part 2).

Model with equations in the form $${px+q=r}$$ and $${p(x+q)=r}$$ .

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Topic B: Solving and Modeling with Inequalities

Solve and graph one-step inequalities.

Write and solve inequalities in the forms $${px+q>r}$$  or  $${px+q<r}$$   and $${p(x+q)>r }$$  or $${p(x+q)<r.}$$

Solve word problems leading to inequalities in the forms $${px+q>r}$$   or $${px+q<r}$$   and $${p(x+q)>r}$$ or $${p(x+q)<r}$$ .

Model with inequalities.

7.EE.B.3 7.EE.B.4.B

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Angle Problems and Solving Equations

Description.

Students use vertical angles, adjacent angles, angles on a line, and angles at a point in a multistep problem to write and solve simple equations

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• Grade 7 Mathematics Module 3, Topic B, Lesson 10: Student Version
• Grade 7 Mathematics Module 3, Topic B, Lesson 10: Teacher Version

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