Linear Equations in One Variable

Solve first-degree equations, equations with brackets, clearing fractions, and word problems.

Full Detailed Notes Video Lesson Worked Examples (1)Take Diagnostic Quiz

Curated Video Lesson

Visual explanation and practical step-by-step walk-through

Watch on YouTube

Comprehensive Study Notes

Aligned with Ghana NaCCA & WAEC BECE syllabus standards

Topic Introduction & Real-World Context:

A linear equation is a mathematical statement asserting that two expressions are equal, containing one unknown variable with power 1. Think of an equation as a two-pan balance scale: as long as you perform the identical operation to both sides, the scale remains balanced. Solving linear equations is one of the most critical exam topics in BECE, appearing both as direct equations and as applied word problems.

What You Will Master in This Lesson (NaCCA Objectives):

Understand the concept of equality and the balance principle of equations.

Solve one-step, two-step, and multi-step linear equations.

Solve equations containing single brackets using the distributive property.

Clear fractional coefficients by multiplying through by the LCM.

Translate English word problems into algebraic linear equations and solve them.

1. The Golden Rule of Equations (Balance Principle)

Whatever operation you perform on the left-hand side (LHS), you MUST perform the exact same operation on the right-hand side (RHS). • Add/subtract the same number from both sides. • Multiply/divide both sides by the same non-zero number.

2. The Transposition Method

When a term moves across the equals sign (=), its operation reverses: • Addition (+) becomes Subtraction (-) • Subtraction (-) becomes Addition (+) • Multiplication (×) becomes Division (÷) • Division (÷) becomes Multiplication (×) Example: 3x + 7 = 22 => 3x = 22 - 7 => 3x = 15 => x = 5.

3. Equations with Brackets and Fractions

• With Brackets: Expand all brackets first, collect like terms, then isolate the variable. • With Fractions: Find the LCM of all denominators and multiply EVERY term on both sides by this LCM. All fractions will cancel out completely!

Common Mistakes Students Make in BECE Examinations:

⚠️Moving a term across the equals sign without changing its sign.

⚠️Multiplying only fractions by LCM and forgetting whole numbers/constants.

⚠️Failing to verify the solution by plugging it back into the equation.

Teacher's BECE Exam Pro-Tips:

⭐Always verify your answer by substituting back into the original equation.

⭐Keep equals signs neatly aligned in a vertical column.

Quick Revision Summary Checklist:

Balance principle: whatever you do to LHS, do to RHS.

Transposition: + becomes -, - becomes +, × becomes ÷.

Multiply EVERY term by LCM to eliminate fractions.

Step-by-Step Worked Examples (1)

Real BECE exam-standard problems with complete solution steps

Example 1: Solving an Equation with Brackets

Problem StatementSolve for x: 3(2x - 4) = 18

Step-by-Step Solution:

Step 1: Expand brackets: 6x - 12 = 18.

Step 2: Add 12 to both sides: 6x = 18 + 12 => 6x = 30.

Step 3: Divide by 6: x = 5.

💡

Key Takeaway / Exam Rule: Always substitute your answer back into original equation to check correctness.

Mastery Diagnostic Quiz

Ready to test your knowledge on Linear Equations in One Variable?

Timed computerized test with instant feedback, scoring, and comprehensive question rationales.

Start Diagnostic Quiz

Previous TopicAlgebraic Expressions and Substitution

Next TopicRatio, Proportion and Sharing