Two step equation Operations

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 = 9 Numerical 3a = 30 Algebraic

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

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

Solving Equations Using Addition or Subtraction: 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.

Solving Equations Using Multiplication or Division Rule 3: If a variable has been multiplied by 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.

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 n on 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 n = 2 Ans: n = 2

= -12 + 7 = -12 + 7 - 7 = -12 - 7 = = 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 j on 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

Try these 7e – 4 = 31