Rearranging Formulas

Introduction

• The goal is to rearrange formulas to isolate a specific variable.
• This is similar to solving equations.
• Steps involve isolating the target variable on one side of the equation.

Example 1: Making 'x' the Subject

1. Given Equation: Solve for x in a formula.
2. Steps:
   • Subtract 4 from both sides:
     • Original: y = 3x + 4
     • Rearranged: y - 4 = 3x
   • Divide by 3:
     • Rearranged: (y - 4) / 3 = x
   • Final Form:
     • x = (y - 4) / 3
   • Note: Using a fraction line is a common way to write the division, eliminating the need for brackets.

Example 2: Making 'b' the Subject

1. Given Equation: Solve for b.
2. Steps:
   • Add 5 to both sides:
     • Original: a = b/3 - 5
     • Rearranged: a + 5 = b/3
   • Multiply by 3:
     • Rearranged: 3(a + 5) = b
   • Final Form:
     • b = 3a + 15
   • Explanation: Multiply the entire left side by 3 and expand the bracket.

Example 3: Isolating 'x' Inside a Bracket

1. Given Equation: Solve for x with x inside a bracket.
2. Steps:
   • Expand the Bracket:
     • Multiply 3 by both 2 and x: 2y = 6 + 3x
   • Subtract 6 from both sides:
     • Rearranged: 2y - 6 = 3x
   • Divide by 3:
     • Rearranged: (2y - 6) / 3 = x
   • Final Form:
     • x = (2y - 6) / 3

Example 4: Isolating 'b'

1. Given Equation: Solve for b.
2. Steps:
   • Subtract 3 from both sides:
     • Original: 6a = b/2 + 3
     • Rearranged: 6a - 3 = b/2
   • Multiply by 2:
     • Rearranged: 2(6a - 3) = b
     • Expand to get: 12a - 6 = b
   • Final Form:
     • b = 12a - 6

Conclusion

• The method involves basic algebraic operations: addition, subtraction, multiplication, and division.
• Aim to simplify and isolate the target variable step by step.
• Use brackets and fraction lines to maintain clarity in operations.

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