Equation with variables on both sides

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 ADD The opposite of subtract is The opposite of multiply is DIVIDE MULTIPLY The opposite of divide is

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.

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

2x = = Continue 8 2 x x 8 Ans: x = 4 By rule 3, a variable is We keep variable x on the Left Handside(LHS) and move constant to the Right Handside(RHS) 2 x x = 8 By rule 3, a variable is multiplied by 2, so divide both sides by 2 x = 4 Ans: x = 4

Example 2: Solve 20 – 4x = 8x + 8 Solution: Equals = 20 – 4x 8x + 8 RHS LHS 20 – 4x = 8x + 8 Constants Constants Variable/Unknown Get the variable on one side of the equation. We keep variable x on the Right Handside(RHS) and move constant to the Left Handside(LHS) By rule 1, 8 is added to the variable 8x , so subtract 8 from both sides of the equation 20 - 4x - 8 = 8x + 8 - 8 -4x + 12 = 8x To remove 4x on LHS add 4x to both sides of the equation By integer rule, if numbers have different sign, subtract the numbers and put sign of bigger number - 4x + 12 + 4x = 8x + 4x

12 = = Continue 12x 12 12 x x Ans: x = 1 By rule 3, a variable is We keep variable x on the Left Handside(LHS) and move constant to the Right Handside(RHS) 12 = 12 x x By rule 3, a variable is multiplied by 12, so divide both sides by 12 1 = x Ans: x = 1

Try These Solve the following 15 + 6x = 45 + 8x 5x + 20 = 6x - 5