Some examples of expressions we have so far worked with are | Class 8 Mathematics Notes

2.3 Reducing Equations to Simpler Form

Sometimes, equations involve fractions or expressions that need to be simplified before solving. This section explains how to reduce such equations to simpler forms by clearing denominators, opening brackets, and combining like terms.

Example 16: Solve (6x + 1)/3 + 1 = (x - 3)/6.

Step 1: Identify the denominators 3 and 6. The LCM is 6. Multiply both sides by 6 to clear fractions: 6 × ((6x + 1)/3 + 1) = 6 × ((x - 3)/6)

Step 2: Distribute 6: 6 × (6x + 1)/3 + 6 × 1 = x - 3

Step 3: Simplify: 2(6x + 1) + 6 = x - 3

Step 4: Open brackets: 12x + 2 + 6 = x - 3

Step 5: Combine constants: 12x + 8 = x - 3

Step 6: Transpose x to LHS and constants to RHS: 12x - x = -3 - 8

Step 7: Simplify: 11x = -11

Step 8: Divide both sides by 11: x = -1

Check by substituting x = -1 into the original equation to verify equality.

Example 17: Solve 5x - 2(2x - 7) = 2(3x - 1) + 7/2.

Step 1: Open brackets: LHS = 5x - 4x + 14 = x + 14 RHS = 6x - 2 + 7/2 = 6x - 4/2 + 7/2 = 6x + 3/2

Step 2: Write equation: x + 14 = 6x + 3/2

Step 3: Transpose terms: 14 - 3/2 = 6x - x

Step 4: Simplify: (28/2) - (3/2) = 5x 25/2 = 5x

Step 5: Divide both sides by 5: x = (25/2) × (1/5) = 5/2

Check by substituting x = 5/2 into the original equation.

This section highlights the importance of simplifying equations by clearing fractions and opening brackets to make solving easier.

📊 Diagram: Figure on page 4 illustrating stepwise simplification and solution.

🧪 Activity: Worked examples demonstrating reduction of complex equations to simpler linear form.

🔗 Connection: Prepares for Exercise 2.2 on solving linear equations involving fractions and brackets.