# MA.8.AR.2.1

Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides.

### Clarifications

Clarification 1: Problem types include examples of one-variable linear equations that generate one solution, infinitely many solutions or no solution.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.AR.2.AP.1a: Identify the steps to solve a given multi-step equation in one variable, with integers coefficients. Include equations with variables on both sides.
MA.8.AR.2.AP.1b: Solve multi-step equations in one variable, with integers coefficients. Include equations with variables on both sides.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Linear Equations - 2:

Students are asked to solve a linear equation in one variable with rational coefficients.

Type: Formative Assessment

Linear Equations - 1:

Students are asked to solve a linear equation in one variable with rational coefficients.

Type: Formative Assessment

Equation Prototypes:

Students are asked to write examples of equations with one solution, no solutions, and infinitely many solutions.

Type: Formative Assessment

Counting Solutions:

Students are asked to identify and explain whether given equations have one solution, no solutions, or infinitely many solutions.

Type: Formative Assessment

Linear Equations - 3:

Students are asked to solve a linear equation in one variable with rational coefficients and variables on both sides of the equation.

Type: Formative Assessment

## Original Student Tutorials

Multi-Step Equations: Part 5 How Many Solutions?:

Learn how equations can have 1 solution, no solution or infinitely many solutions in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• [CURRENT TUTORIAL] Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-Step Equations: Part 4 Putting it All Together:

Learn alternative methods of solving multi-step equations in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• [CURRENT TUTORIAL] Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-step Equations: Part 3 Variables on Both Sides:

Learn how to solve multi-step equations that contain variables on both sides of the equation in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• [CURRENT TUTORIAL] Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-Step Equations: Part 2 Distributive Property:

Explore how to solve multi-step equations using the distributive property in this interactive tutorial.

This is part two of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• [CURRENT TUTORIAL] Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-Step Equations: Part 1 Combining Like Terms:

Learn how to solve multi-step equations that contain like terms in this interactive tutorial.

This is part one of five in a series on solving multi-step equations.

• [CURRENT TUTORIAL] Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Justifiable Steps:

Learn how to explain the steps used to solve multi-step linear equations and provide reasons to support those steps with this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

Solve a Consecutive Integer Problem Algebraically:

This video will show how to solve a consecutive integer problem.

Type: Tutorial

## MFAS Formative Assessments

Counting Solutions:

Students are asked to identify and explain whether given equations have one solution, no solutions, or infinitely many solutions.

Equation Prototypes:

Students are asked to write examples of equations with one solution, no solutions, and infinitely many solutions.

Linear Equations - 1:

Students are asked to solve a linear equation in one variable with rational coefficients.

Linear Equations - 2:

Students are asked to solve a linear equation in one variable with rational coefficients.

Linear Equations - 3:

Students are asked to solve a linear equation in one variable with rational coefficients and variables on both sides of the equation.

## Original Student Tutorials Mathematics - Grades 6-8

Multi-Step Equations: Part 1 Combining Like Terms:

Learn how to solve multi-step equations that contain like terms in this interactive tutorial.

This is part one of five in a series on solving multi-step equations.

• [CURRENT TUTORIAL] Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Multi-Step Equations: Part 2 Distributive Property:

Explore how to solve multi-step equations using the distributive property in this interactive tutorial.

This is part two of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• [CURRENT TUTORIAL] Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Multi-step Equations: Part 3 Variables on Both Sides:

Learn how to solve multi-step equations that contain variables on both sides of the equation in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• [CURRENT TUTORIAL] Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Multi-Step Equations: Part 4 Putting it All Together:

Learn alternative methods of solving multi-step equations in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• [CURRENT TUTORIAL] Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Multi-Step Equations: Part 5 How Many Solutions?:

Learn how equations can have 1 solution, no solution or infinitely many solutions in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• [CURRENT TUTORIAL] Part 5: How Many Solutions?

## Original Student Tutorials Mathematics - Grades 9-12

Justifiable Steps:

Learn how to explain the steps used to solve multi-step linear equations and provide reasons to support those steps with this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Multi-Step Equations: Part 5 How Many Solutions?:

Learn how equations can have 1 solution, no solution or infinitely many solutions in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• [CURRENT TUTORIAL] Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-Step Equations: Part 4 Putting it All Together:

Learn alternative methods of solving multi-step equations in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• [CURRENT TUTORIAL] Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-step Equations: Part 3 Variables on Both Sides:

Learn how to solve multi-step equations that contain variables on both sides of the equation in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• [CURRENT TUTORIAL] Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-Step Equations: Part 2 Distributive Property:

Explore how to solve multi-step equations using the distributive property in this interactive tutorial.

This is part two of five in a series on solving multi-step equations.

• Click HERE to open Part 1: Combining Like Terms
• [CURRENT TUTORIAL] Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Multi-Step Equations: Part 1 Combining Like Terms:

Learn how to solve multi-step equations that contain like terms in this interactive tutorial.

This is part one of five in a series on solving multi-step equations.

• [CURRENT TUTORIAL] Part 1: Combining Like Terms
• Click HERE to open Part 2: The Distributive Property
• Click HERE to open Part 3: Variables on Both Sides
• Click HERE to open Part 4: Putting It All Together
• Click HERE to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Justifiable Steps:

Learn how to explain the steps used to solve multi-step linear equations and provide reasons to support those steps with this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

Solve a Consecutive Integer Problem Algebraically:

This video will show how to solve a consecutive integer problem.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.