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Mastering Two-Step Equations with Division Rules

Learn how to solve two-step equations by applying division rules and transposing numbers effectively. Understand the importance of balancing the equation and practice with step-by-step examples.

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Mastering Two-Step Equations with Division Rules

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  1. solve two step equation using division

  2. Rules to apply while solving Equations Rule 1: If a number has been added to the variable, subtract that number from both sides of the equation. Rule 2: If a number has been subtracted from the variable, add that number to both sides of the equation. Rule 3: If a non-zero number has been multiplied to the variable, divide both sides by that number. Rule 4: If a variable has been divided by a number, multiply both sides by that number. Let us identify the operation to separate the variable in following examples and learn to solve a little later.

  3. Transposing a number – Changing the side of a number • While solving Equations, commonly used operation is adding or • subtracting the same number on both sides of equation. • Instead of adding or subtracting a number on both sides of an • equation, we can Transpose the number. • Transposing a number (changing the side of a number) is the • same as adding or subtracting the number from both sides • While transposing a number, we must change its sign. + 5 when transposed becomes -5 -7 when transposed becomes +7

  4. Transposing step can be used in place of adding or subtracting a number to both sides of equation Let us check by solving same Equation using Adding a number both sides and Transposing method as first step Or Adding both sides Transposing a Number Equation 2y – 12 = 8 Step 1: Add 12 both sides 2y – 12 + 12 = 8 + 12 2y = 20 Equation 2y – 12 = 8 Step 1: Transpose -12 from LHS to RHS 2y – 12 = 8 On Transposing -12 becomes +12 2y = 8 + 12 2y = 20 -12 + 12 = 0 Note by applying both methods, we get 2y = 20 2y = 2 *y Solving further, Step 2: By Rule 3, divide both sides by 2 Cancel 2 in LHS = 20 ÷ 2 = 10 RHS Ans: Solution of equation 2y – 12 = 8 is y = 10

  5. Transposing step can be used in place of adding or subtracting a number to both sides of equation Let us check by solving an Equation using Subtracting a number both sides and Transposing method as first step Or Subtracting both sides Transposing a Number Equation 5x + 11 = 26 Step 1: Subtract 11 both sides 5x + 11 – 11 = 26 - 11 Equation 5x + 11 = 26 Step 1: Transpose +11 from LHS to RHS 5x + 11 = 26 On Transposing + 11 becomes -11 5x = 26 – 11 +11 –11 = 0 5x = 15 5x = 15 Note by applying both methods, we get 5x = 15 5x = 5*x Solving further, Step 2: By Rule 3, divide both sides by 5 Cancel 5 in LHS = 15 ÷ 5 = 3 RHS Ans: Solution of equation 5x + 11 = 26 is x = 3

  6. Example 1: Solve: 5x – 7 = 38 Transposing a Number Adding both sides Given:5x – 7 = 38 Step 1: By Rule 2, add 7 to LHS and RHS 5x – 7 + 7 = 38 + 7 5x = 45 Given: 5x – 7 = 38 Step 1: 5x – 7 = 38 Transposing (-7) from LHS to RHS as +7 5x = 38 + 7 5x = 45 Step 2: By Rule 3, variable x is multiplied by 5, so divide both sides by 5 5x = 45 5x = 5 * x Step 3: LHS- Cancel 5 variable is separated RHS Divide 45 by 5 Ans: x = 9 x = 9

  7. Example 2: Solve: 19 = 11x – 2 Transposing a Number Adding both sides Rewrite Equation with variable in LHS 11x – 2 = 19 Step 1: 11x – 2 = 19 Transposing (-2) from LHS to RHS as +2 11x = 19 + 2 11x = 21 Rewrite Equation With variable in LHS 11x – 2 = 19 Step 1: By Rule 2, add 2 to 11x – 2 +2 = 19 + 2 LHS and RHS 11x = 21 Step 2: By Rule 3, variable x is multiplied by 11, so divide both sides by 11 11x = 21 11x = 11 * x Step 3: LHS- Cancel 11 variable is separated RHS :Write the Fraction as such Ans:

  8. Example 3: Solve: 8 + 2y = - 44 Transposing a Number Subtracting both sides Rewrite Equation with variable in LHS 2y + 8 = - 44 Step 1: 2y + 8 = -44 Transposing (+ 8) from LHS to RHS as -8 2y = - 44 -8 2y = -52 Rewrite Equation With variable first 2y + 8 = -44 Step 1: By Rule 1, Subtract 8 2y + 8 – 8 = - 44 -8 from LHS and RHS 2y = -52 Step 2: By Rule 3, variable y is multiplied by 2, so divide both sides by 2 2y = - 52 2y = 2 * y Step 3: LHS- Cancel 2 variable is separated RHS : Divide and write answer with (-) sign Ans:

  9. Example 4: Solve: 77 = 3x + 7 Transposing a Number Subtracting both sides Rewrite Equation with variable in LHS 3x + 7 = 77 Step 1: 3x + 7 = 77 Transposing (+ 7) from LHS to RHS as -7 3x = 77 - 7 3x = 70 Rewrite Equation With variable in LHS 3x + 7 = 77 Step 1: By Rule 1, Subtract 7 3x + 7 -7 = 77 – 7 from LHS and RHS 3x = 70 Step 2: By Rule 3, variable x is multiplied by 3, so divide both sides by 3 3x = 70 3x = 3 * x Step 3: LHS- Cancel 3 variable is separated RHS : Write answer as fraction as such Ans:

  10. Try these 1.Solve: 9x + 2 = 46 2. Solve: 2x – 3 = 17 Solve: 11 = 26x – 1

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