# Equations and Inequalities

## Objective

Define and identify solutions to equations.

## Common Core Standards

### Core Standards

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• 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.

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• 6.EE.A.1

• 6.EE.A.2

## Criteria for Success

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1. Define a solution to an equation as the value of the variable that, when substituted in, makes the equation a true statement.
2. Use substitution to determine if a given value for a variable is a solution to an equation.
3. Make use of structure in expressions and equations to reason about the value of the variable (MP.7).

## Tips for Teachers

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#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example) and Anchor Problem 2 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Determine if the equations are true or false when the number given is used for the value of the variable.

1.   ${12x=84}$; for when ${x=7}$
2.  ${y-10=50}$; for when ${y=40}$
3.   ${{1\over2}m=16}$; for when ${ m=32}$
4.   ${3(x-1)=27}$; for when ${x=9}$

### Problem 2

Which value of $x$ from the set below is the solution to the equation $4x-14=38$?

{6, 10, 12, 13, 15}

### Problem 3

Below are some equations that each contain a variable. A list of values is also shown. Think about what each equation means to find a solution in the list of values. #### References

Open Up Resources Grade 6 Unit 6 Lesson 22.3 “Using Structure to Find Solutions”

Modified by The Match Foundation, Inc.

## Problem Set

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

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Which equations below have a solution ${x=4}$?

1.   ${14-x=14}$
2.   ${2x+5=9}$
3.   ${4x=1}$
4.   ${ 4x=16}$
5.   ${ 3x-2=10}$
6.   ${{1\over2}x=8}$

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