Solving Equations Using Addition or Subtraction Objective Students

Solving Equations Using Addition or Subtraction Objective: Students will solve linear equations using addition and subtraction.

Algebra Standards: 8. EE. 7 Solve Linear Equations in one variable

Vocabulary Equivalent equations: are equations that have the same solution(s). Inverse operations: are operations that undo each other, such as addition and subtraction. Linear equation: The exponent of the variable(s) is one.

What is an Equation? Equation - a balanced statement of equality between two quantities. 4+3=7 4+3 = fulcrum 7

What is an Equation? 4+3 -3 = 7 -3

What is an Equation? 4 = 4 Perform the same operation to both sides to keep the equation balanced.

What is an Equation? This property can be used to solve variable equations. x+6 -6 = 11 -6 x = 5 Algebraic Approach 0 x + 6 = 11 -6 -6 x =5

Transforming Equations Operation • Add the same number to each side • Subtract the same number from each side • Simplify one or both sides Original Equation Equivalent Equation x– 3=5 3 Add ___ 8 x = ___ x + 6 = 10 6 Subtract ___ 4 x = ___ x=8– 3 Simplify 5 x = ____

#1 Add to Each side of an Equation 0 Solve x – 9 = -20 +9 +9 x = - 11

#2 Simplify first Solve n – (-8) = -2 0 n + 8= -2 -8 -8 n = - 10

Check Point: Solve the equation. 0 1) x – 7 = -15 +7 +7 x = -8 0 3) -7 = 10 + y -10 - 17 = y 2) n – (-6) = 4 0 n +6 = 4 -6 -6 n = -2 4) 5 – (-z) = 21 0 5 + z = 21 -5 -5 z = 16

Check Point: Solve the equation. 0 5) m – (-3) = 14 0 m + 3 = 14 -3 -3 m = 11 6) -8 = -b + (-2) +2 +2 - 6 = -b 1 -6 = (-1)b -1 -1 6=b