
Simplifying with Addition and Subtraction: We can use addition and subtraction to get all the terms with variables on one side of an equation, and all the numeric terms on the other. The equations 3x = 17, 21 = y, and z/12 = 24 each have a variable term on one side of the '=' sign, and a number on the other. The equations x + 3 = 12, 21 = 30  y, and (z + 2) × 4 = 10 do not. We usually do this after simplifying each side using the distributive rules, eliminating parentheses, and combining like terms. Since addition is associative, it can be helpful to add a negative number to each side instead of subtracting. Examples:
For the equation 8 = 20  z, we can add z to both sides to get 8 + z = 20  z + z => 8 + z = 20. Now subtracting 8 from both sides, 8 + z  8 = 20  8 Therefore, z = 12 Simplifying by Multiplication When solving for a variable, we want to get a solution like x = 3 or z = 198 etc. When a variable is divided by some number, we can use multiplication on both sides to solve for the variable.
Example: Simplifying by Division When solving for a variable, we want to get a solution like x = 9 or y = 21 etc. When a variable is multiplied by some number, we can use division on both sides to solve for the variable. Example: Solve for x in the equation 7x = 280. Since the x on the left side is being multiplied by 7, we can divide both sides by 7 to solve for x: 7x ÷ 7 = 280 ÷ 7 (7x)/7 = 280 ÷ 7 x/1 = 40 x = 40. Note: Dividing by 7 is the same as multiplying both sides by 1/7. Directions: Solve the following equations and enter the solution. Also write at least 10 examples of your own. 