Home›Lesson Plans›Mathematics›Algebra I · Grade 9

Solving Multi-Step Equations: Isolating the Variable

Students master the core skill of algebra — solving for an unknown — by undoing operations in the right order to isolate the variable, even when it appears on both sides of the equation.

Grade 9Equations50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Solve multi-step equations.
  • ✓Use inverse operations.
  • ✓Solve equations with variables on both sides.
  • ✓Check a solution.
Essential Question

An equation is a balance scale: whatever you do to one side, you must do to the other. How do you work backwards to find the value that makes it balance?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

Solve for x

Project each equation and have students solve for x. The tool shows the steps — undo the operations in reverse order to isolate the variable.

🧮 Solve each equation — find xTry it
Solve for x. Undo the operations to isolate the variable.
The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — The Balance

5 min

An equation is a scale — how do you find the hidden weight?

👩‍🏫 Teacher Moves

  • Show an equation as a balance.
  • Ask how to isolate x.
  • Set the goal: solving equations.

🎒 Student Actions

  • Picture the balance.
  • Predict the steps.
  • Guess the method.
2

I Do — Inverse Operations

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Undo addition/subtraction first.
  • Then undo multiplication/division.
  • Keep both sides equal.

🎒 Student Actions

  • Follow the steps.
  • Undo operations.
  • Keep it balanced.
3

We Do — Solve Together

13 min

Class uses Solve for x.

👩‍🏫 Teacher Moves

  • Work through each equation.
  • Handle variables on both sides.
  • Check each solution.

🎒 Student Actions

  • Solve each.
  • Move variables.
  • Check the answer.
4

You Do — On Your Own

12 min

Students solve equations.

👩‍🏫 Teacher Moves

  • Assign multi-step equations.
  • Include distribution and both sides.
  • Check solutions.

🎒 Student Actions

  • Solve them.
  • Show the steps.
  • Check answers.
5

Close — Close

5 min

One equation.

👩‍🏫 Teacher Moves

  • Give an equation to solve.
  • Show the steps.
  • Hand out the exit ticket.

🎒 Student Actions

  • Solve it.
  • Explain the steps.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School: Algebra I).

CCSS
A-REI.3

Solve linear equations and inequalities in one variable.

CCSS
A-REI.1

Explain each step in solving an equation.

CCSS
A-CED.1

Create equations in one variable and use them to solve problems.

CCSS
A-REI.B

Solve equations and inequalities in one variable.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Show the balance visually.
  • Sentence frame: “To undo ___, I ___.”
  • Use inverse-operation cards.

Support & Access

IEP / 504
  • Start with two-step equations.
  • Provide a steps checklist.
  • Check by substitution.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Solve equations with fractions.
  • Solve literal equations for a variable.
  • Write an equation from a word problem.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻Solve for x
  • ⚖️A balance model
  • 🧮Calculators
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

equationa statement that two expressions are equalvariablea letter standing for an unknowninverse operationthe operation that undoes anotherisolateto get the variable alonecoefficientthe number multiplying a variableconstanta fixed numberdistributeto multiply across parenthesessolutionthe value that makes it true
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Solve: 4x + 7 = 19.
x = 3 (subtract 7, then divide by 4).
QUESTION 2
When solving, what should you do first: undo addition or undo multiplication?
Undo addition/subtraction first, then multiplication/division (reverse order of operations).
QUESTION 3
How can you check your solution?
Substitute it back into the original equation and see if both sides are equal.

Going deeper? Equations with fractions.

Have students clear fractions by multiplying every term by the common denominator, then solve. A printable equations sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Solving Multi-Step EquationsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Solving Multi-Step EquationsQuiz
Score: 0
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Solving Multi-Step EquationsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: coefficient, constant, distribute, equation, inverse operation, isolate, solution, variable
  1. the operation that undoes another
  2. a statement that two expressions are equal
  3. to get the variable alone
  4. the value that makes it true
  5. a fixed number
  6. a letter standing for an unknown
  7. the number multiplying a variable
  8. to multiply across parentheses

Part B · Show what you learned

  1. Solve: 4x + 7 = 19.
  2. When solving, what should you do first: undo addition or undo multiplication?
  3. How can you check your solution?
Answer key — Part A: 1) inverse operation · 2) equation · 3) isolate · 4) solution · 5) constant · 6) variable · 7) coefficient · 8) distribute
Part B: 1) x = 3 (subtract 7, then divide by 4). 2) Undo addition/subtraction first, then multiplication/division (reverse order of operations). 3) Substitute it back into the original equation and see if both sides are equal.