CCSS.MATH.CONTENT.8.EE.C.7✓ Wyoming Department of Education AlignedAcademic Year 2026–27
Solving Linear Equations in One Variable
Master solving multi-step linear equations with variables on both sides using inverse operations, distributive property, and balancing principles.
Why It Matters:Forms the foundational mathematics for machine learning algorithms, game physics engines, and economic balancing models.
Curated Video Instruction
● Verified Active EmbedSTEP-BY-STEP PROOF
Worked Example
Solve for x: 5x - 8 = 2x + 13
1
Subtract 2x from both sides
3x - 8 = 13
Collect all variable terms onto the left side of the equation.
2
Add 8 to both sides
3x = 21
Isolate variable term by eliminating constant on left side.
3
Divide both sides by 3
x = 7
Multiply by reciprocal (or divide) to yield solution.
✓Verification Check
Substitute x = 7 back into original equation 5x - 8 = 2x + 13:
Left side: 5(7) - 8 = 35 - 8 = 27
•
Right side: 2(7) + 13 = 14 + 13 = 27
⚠️ Common Pitfalls & Misconceptions
Sign errors during subtraction across the equal sign
✗ 5x - 8 = 2x + 13 => 7x = 5✓ 5x - 2x = 3x, and 13 + 8 = 21 => 3x = 21
Remember to apply inverse operations to both sides equally.
INTERACTIVE DRILLS
Guided Practice
Practice Question1 of 1
Step-by-step Feedback
Solve for x: 4x + 7 = 2x + 19
MASTERY BENCHMARK
Official Assessment Quiz
Formal Assessment
Solving Linear Equations in One Variable
Passing Criteria:70% or higher
Question 1 of 1
What is the first step to solve: 7x - 4 = 3x + 16?
Education to Career Navigation
Where This Lesson Leads
Software Engineers and Aerospace Architects use linear equations daily to model dynamic physical systems.