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Mastering Two-Step Equations: Operations & Steps

Learn the basics of solving two-step equations, including addition, subtraction, multiplication, and division rules. Understand how to isolate the variable and apply inverse operations to find the unknown values.

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Mastering Two-Step Equations: Operations & Steps

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  1. Two step equation Operations

  2. Introduction What is an equation? • An equation is a mathematical statement that • shows 2 quantities are equal. An equation contains • an equal sign. • 12 – 3 = 9Numerical • 3a = 30 Algebraic

  3. Steps for Solving One-Step Equations 1) Get the variableon one side of the equation. 2) You always perform the same operationto both sidesof an equation. 3) To undo an operation you perform its opposite operationto both sides of the equation.

  4. Opposite operations SUBTRACT The opposite of add is The opposite of subtract is ADD The opposite of multiply is DIVIDE The opposite of divide is MULTIPLY

  5. Solving Equations Using Addition or Subtraction: Rule 1: If a number has been addedto 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.

  6. Solving Equations Using Multiplication or Division Rule 3: If a variable has been multipliedby a non zero number, divide both sides by that number. Rule 4: If a variable has been divided by a number, multiply both sides by that number.

  7. Example 1: Solve 4n + 7 = 15 Solution: Equals = 4n + 7 15 RHS LHS Variable/ Unknown 4n + 7 = 15 Constants Get the variable on one side of the equation. We keep variable non the Left Handside(LHS) and move constant to the Right Handside(RHS) 4n + 7 - 7 = 15 - 7 By rule 1, 7 is added to the variable, so subtract 7 from both sides of the equation By integer rule, if numbers have different sign, subtract the numbers and put sign of bigger number 4n = 8 By rule 3, a variable is multiplied by 4,so divide b oth sides by 4 Hint: 4n = 4 x n Ans: n = 2 n = 2

  8. Example 2: Solve Solution: Equals = -12 RHS LHS Variable/ Unknown + 7 = -12 Constants Get the variable on one side of the equation. We keep variable jon the Left Handside(LHS) and move constant to the Right Handside(RHS) + 7 - 7 = -12 - 7 By rule 1, 7 is added to the variable, so subtract 7 from both sides of the equation By integer rule, if numbers have different sign, subtract the numbers and put sign of bigger number = -19 = -19 x 2 By rule 4, a variable is divided by 2,so multiply both sides by 2 Ans: j = -38 j = -38

  9. Try these • 7e – 4 = 31

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