Objective - To solve simple equations involving addition and subtraction. Identity Property of Addition additive identity Equation - A mathematical sentence that shows two expressions are equal. = 8 + 4 12 “fulcrum” Equations must always stay perfectly balanced.

Determine which value is the correct solution to the equation.

Addition Property of Equality If a = b, then a + c = b + c or Given a = b and c = c then a + c = b + c Subtraction Property of Equality If a = b, then a - c = b - c or Given a = b and c = c then a - c = b - c

x + 3 = 7 Heavier - 3

x = 7 Heavier

x = 7 Heavier

x = 7 Heavier

x = 7 Heavier

x + 3 = 7 - 3 = x 4 Algebraically, x + 3 = 7 x + 3 = 7 -3 -3 x + 3 - 3 = 7 - 3 x = 4 x = 4

Rules for Transforming Equations 1) Goal: Isolate the variable on one side of the equation. 2) Always perform the same operation to both sides of an equation. 3) To undo an operation, perform its opposite operation to both sides of the equation.

Solve the equations below. 1) x + 3 = 10 4) 13 = x + 5 - 3 - 3 - 5 - 5 x = 7 8 = x 2) y - 8 = 11 5) 12 = n - 3 +8 +8 +3 +3 y = 19 15 = n 3) n + 5 = 11 6) 11 + 3 = k - 5 - 5 14 = k n = 6

Translate the sentence into an equation and solve. 1) The sum of k and 13 is 28. k + 13 = 28 - 13 - 13 k = 15 2) Five is the difference of t and 4. 5 = t - 4 +4 +4 9 = t

Five-Step Plan 1) Read the problem. Draw a picture. Make a chart. 2) Determine the unknowns. Define an unknown with a variable. Define all other unknowns in terms of first variable. 3) Write an equation involving the variable. 4) Solve the equation. 5) Check your answer.

1) Matt scored a 85 on his last test. This is 16 points higher than he scored on his first test. What was his score on the first test? Let t = first test score

Define a variable, write an algebraic equation, and solve. 2) A gazelle can run at a speed of 50 mph. This is 10mph slower than the speed of a cheetah. What is the speed of a cheetah? Let x = the speed of a cheetah 50 = x - 10 +10 +10 60 = x cheetah speed = 60

Define a variable, write an algebraic equation, and solve. 3) The Sears Tower is 110 stories tall. This is 8 stories taller than the Empire State Building. How many floors is the Empire State Building? Let x = the # of stories in Empire State 110 = x + 8 -8 -8 102 = x # Floors in Empire State = 102

Define a variable, write an algebraic equation, and solve. 4) A submarine is 50 meters below the surface of the ocean. A scuba diver is 5 meters below the surface. Write an equation to find their difference in elevation and solve. Let x = difference in elevation -50 + x = -5 +50 +50 x = 45 Difference in elevation = 45