Free Linear Equation Worksheets (Grades 6-9)

Practice linear equation (Grades 6-9) with free printable PDF worksheets. 4 pre-packaged classroom sets with 100% verified step-by-step answer keys, plus an unlimited live customizer for teachers and homeschoolers.

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PanMaths.comLinear Equation Worksheets • Set A (Standard)

Name: __________________________

Date: _____________ Period: ____

Score: _____ / 10

Directions: Solve each problem carefully. Show all intermediate work in the workspace provided.

x−2=10

5x=30

x−2=13

2x=18

x−6=15

x+6=10

6x=24

x+5=6

x−4=2

10.

x−8=2

PanMaths.com • Free Printable Math WorksheetsPage 1 of 2

PanMaths.comAnswer Key & Worked Solutions • Set A (Standard)

Answer Key

Total Problems: 10

Teacher & Parent Guide: Intermediate evaluation steps are provided for step-by-step grading and student self-correction.

x−2=10= x = 12

1. Inverse Operation: Add 2 to both sides

2. Simplify: x = 10 + 2 → x = 12

3. Proof Check: 12 − 2 = 10 ✅

5x=30= x = 6

1. Inverse Operation: Divide both sides by 5

2. Simplify: x = 30 / 5 → x = 6

3. Proof Check: 5(6) = 30 ✅

x−2=13= x = 15

1. Inverse Operation: Add 2 to both sides

2. Simplify: x = 13 + 2 → x = 15

3. Proof Check: 15 − 2 = 13 ✅

2x=18= x = 9

1. Inverse Operation: Divide both sides by 2

2. Simplify: x = 18 / 2 → x = 9

3. Proof Check: 2(9) = 18 ✅

x−6=15= x = 21

1. Inverse Operation: Add 6 to both sides

2. Simplify: x = 15 + 6 → x = 21

3. Proof Check: 21 − 6 = 15 ✅

x+6=10= x = 4

1. Inverse Operation: Subtract 6 from both sides

2. Simplify: x = 10 − 6 → x = 4

3. Proof Check: 4 + 6 = 10 ✅

6x=24= x = 4

1. Inverse Operation: Divide both sides by 6

2. Simplify: x = 24 / 6 → x = 4

3. Proof Check: 6(4) = 24 ✅

x+5=6= x = 1

1. Inverse Operation: Subtract 5 from both sides

2. Simplify: x = 6 − 5 → x = 1

3. Proof Check: 1 + 5 = 6 ✅

x−4=2= x = 6

1. Inverse Operation: Add 4 to both sides

2. Simplify: x = 2 + 4 → x = 6

3. Proof Check: 6 − 4 = 2 ✅

10.

x−8=2= x = 10

1. Inverse Operation: Add 8 to both sides

2. Simplify: x = 2 + 8 → x = 10

3. Proof Check: 10 − 8 = 2 ✅

PanMaths.com • Answer Key & SolutionsPage 2 of 2

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How to Create & Print Custom Worksheets in 3 Steps

Every generated sheet includes student name, date, score lines, and a complete answer key!

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1. Set Options & Count

Select difficulty (Easy, Medium, Hard) and choose your exact problem count (8, 12, 16, or 20 problems per sheet).

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2. Generate & Review

Click "Shuffle" to generate fresh randomized questions. Student name, date, and score blanks are added automatically.

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3. Print with Answer Key

Print clean 8.5"×11" pages. Includes a detachable verified answer key for 1-minute grading or student self-checking!

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What Every Sheet Includes: Name & Date headers, organized problem numbering, ample student write-in workspace, and a step-by-step verified grading key!

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Worksheet Info

Categoryalgebra

Grade LevelGrades 6-9

DifficultyCustomizable

Time10-15 minutes

Skills Practiced

✓ Math fluency
✓ Mental math speed

🎮 Interactive Warm-Up

1-Step & 2-Step Linear Equations Blitz

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Related Worksheets

📄 Cube Root (∛x)View →📄 Factorial (n!)View →📄 Adding and Subtracting IntegersView →📄 Multiplying and Dividing IntegersView →

Strategies

SADMEP Order: Undo addition/subtraction before multiplication/division.
The Golden Scale Law: Always perform identical operations to both sides of the equals sign.
Substitution Check: Plug the calculated x value back into the original equation to verify.

Worksheet Facts by Grade Level

Grade Level	Common Core Standard	Target Operations & Complexity	Recommended Drills
Grade 6	CCSS.MATH.CONTENT.6.EE.B.7	Solve real-world one-step linear equations involving non-negative rational numbers	Set A (Standard 10 Problems)
Grade 7	CCSS.MATH.CONTENT.7.EE.B.4	Solve two-step linear equations (px + q = r) fluently with positive and negative integers	Set B (Two-Step Practice)
Grade 8	CCSS.MATH.CONTENT.8.EE.C.7	Solve linear equations in one variable with variables on both sides and distributive grouping	Set C (Challenging Drills)
High School Algebra 1	CCSS.MATH.CONTENT.HSA.REI.B.3	Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters	Set C & Unlimited Studio custom drills

The 3 Core Rules for Solving Linear Equations

Solving for the unknown variable x requires isolating the variable using reversible inverse operations:

1. The Golden Scale Law: Whatever mathematical operation you perform on the left side of the equation (addition, subtraction, multiplication, division), you MUST perform on the right side.
2. SADMEP Order (Reverse PEMDAS): Always eliminate constants via addition or subtraction before dividing by the variable's coefficient.
3. Proof Verification: Substitute your calculated solution x back into the original equation to verify that Left Hand Side = Right Hand Side.

Step-by-Step Breakdown: 2-Step Equations (ax + b = c)

A standard two-step equation requires exactly two inverse moves:

Step	Algebraic Action	Example: 3x + 7 = 22
Step 1	Subtract constant `b` from both sides	3x + 7 − 7 = 22 − 7 → 3x = 15
Step 2	Divide both sides by coefficient `a`	3x / 3 = 15 / 3 → x = 5
Step 3	Proof check substitution	3(5) + 7 = 15 + 7 = 22 ✅

Equations with Variables on Both Sides (ax + b = cx + d)

When variables appear on both sides of the equals sign, gather all variable terms onto the side with the larger coefficient first:

5x + 3 = 2x + 18 → (5x − 2x) = 18 − 3 → 3x = 15 → x = 5

This guarantees that the resulting coefficient remains positive, preventing negative sign calculation errors.

Benefits of Mastery

⚖️ Core Algebraic Fluency

Builds intuition for equation balance, variable isolation, and inverse operations.

🎯 CCSS Standard Aligned

Directly maps to 6.EE.B.7, 7.EE.B.4, 8.EE.C.7, and HSA-REI.B.3 across Grades 6 to 9.

🧠 Logical Deductive Reasoning

Develops disciplined step-by-step problem-solving habits essential for high school STEM.

✅ Step-by-Step Answer Keys

Every generated PDF includes full intermediate inverse operation steps for instant grading.

Frequently Asked Questions

What is the difference between a 1-step and 2-step linear equation?

A 1-step equation requires only one inverse operation to solve (e.g. x + 5 = 12 → subtract 5). A 2-step equation requires two operations: first adding/subtracting the constant, then multiplying/dividing the coefficient (e.g. 2x + 4 = 14).

Are all solutions on these worksheets clean integers?

Yes. All generated linear equation problem sets are mathematically calibrated to yield clean integer solutions (e.g. x = 5, x = −3), preventing awkward repeating decimal confusion.

Do the answer keys show step-by-step inverse operations?

Yes. Every generated answer key details each inverse operation step, the simplified intermediate equation, and a final proof check.

Can I print equations with variables on both sides?

Yes. Set C defaults to equations with variables on both sides (ax + b = cx + d). You can also customize difficulty in the Studio.