1.8: Intro to Equations Equation: A mathematical sentence that uses the equal ( = ) sign. Ex: 3x=12, -1(x + 5) = 8, Open Sentence: An equation.

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Presentation transcript:

1.8: Intro to Equations Equation: A mathematical sentence that uses the equal ( = ) sign. Ex: 3x=12, -1(x + 5) = 8, Open Sentence: An equation that contains one or more variables. Ex: 3x+ 7 = 21, 2y -5 = y + 8

Solution: The value of the variable that makes the equation true. Ex: 3x+5 = 20  3x = 20-5  x = 15/3 x = 5

GOAL:

Identifying solutions: We must be able to show if a digit is a solution to an equation. Ex: Decide if the given number is a solution: 5b + 1 = 16; -3 Solution: To show if b=3 is a solution, we must substitute: 5( -3 ) + 1 = 16 -15 + 1 = 16 –14= 16 Since -14 is not equal to 16, b=-3 is not a solution to the equation.

Ex: is m = ½ a solution to 6m – 8 = -5? Solution: To show if m= ½ is a solution, we must substitute: 6( ½ ) – 8 = –5 3– 8 = –5 – 5 = –5 Since -5 is equal to -5, m=½ is a solution to the equation.

REAL-WORLD: The equation 25 + 0.25p = c gives the cost in dollars that a store charges to deliver an appliance that weights p pounds. Use the equation an a table to find the weight of an appliance that costs $55 to deliver.

SOLUTION: Using the given equation and the table we have: P in lbs 25 + 0.25p c 50 25 + 0.25(50) $ 37.5 100 25 + .25(100) $50 110 25 + .25(110) $52.50 120 25 + .25(120) $55 Therefore an appliance that weights 120 lbs will cost $55 to deliver.

Solving Equations: To solve an equation we must ISOLATE the variable involved by using opposite math operations to the ones the equation has. Ex: Find the solution to the equations: a) 2x - 3 = 11 b) x + 4 = - 2

Solution: a) 2x – 3 = 11 b) x + 4 = – 2 + 3 + 3 – 4 = –4 2x = 14 + 3 + 3 – 4 = –4 2x = 14 x = –6 x = 14/2 x = 7 Don’t forget to CHECK to make sure you got the correct solution.

CHECK: Replace your answer in the original equation to make sure you got the correct solution. Ex: a) 2x - 3 = 11 b) x + 4 = – 2 2(7) – 3 = 11 (– 6 )+ 4 = – 2 14 – 3 = 11 – 2 = –2 11 = 11 Both integers, the left and the right, coincide thus we have gotten the correct solution.

VIDEOS: Intro to Equations Solving: http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/e/one_step_equations

Class Work: Pages: 56 – 58 Problems: As many as you need to master the concepts.