Linear Equations: Using the Properties Together

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Presentation transcript:

Linear Equations: Using the Properties Together Section 2.2 Linear Equations: Using the Properties Together

Section 2.2 Objectives 1 Use the Addition and Multiplication Properties of Equality to Solve Linear Equations 2 Combine Like Terms and Use the Distributive Property to Solve Linear Equations 3 Solve a Linear Equation with the Variable on Both Sides of the Equation 4 Use Linear Equations to Solve Problems

Solving Linear Equations Example: Solve the linear equation 3x  9 = 24. 3x  9 = 24 3x  9 + 9 = 24 + 9 Add 9 to both sides of the equation. 3x = 15 Divide both sides of the equation by 3 x = 5 3(5)  9 = 24 Check your answer in the original equation. 15  9 = 24 24 = 24 

Solving by Combining Like Terms Example: Solve the equation 3x  8 = 2x  15 3x  8 = 2x  15 3x = 2x  7 Add 8 to both sides. x =  7 Subtract 2x from both sides. 3(7)  8 = 2(7)  15 Check your answer in the original equation. 21  8 = 14  15 29 = 29 

Using the Distributive Property Example: Solve the equation 12  2x  3(x + 2) = 4x + 12 – x. 12  2x  3(x + 2) = 4x + 12 – x 12  2x  3x  6 = 4x + 12 – x Use the Distributive Property. 6  5x = 3x + 12 Combine like terms. 6 = 8x + 12 Add 5x to both sides. – 6 = 8x Subtract 12 from both sides. Divide both sides by 8 and simplify. Be sure to check your answer.

Solving a Linear Equation Step 1: Remove any parentheses using the Distributive Property. Step 2: Combine like terms on each side of the equation. Step 3: Use the Addition Property of Equality to get all variables on one side and all constants on the other side. Step 4: Use the Multiplication Property of Equality to get the coefficient of the variable to equal 1. Step 5: Check the solution to verify that it satisfies the original equation.

Solving Problems A Chunky Cheeseburger contains 12 more grams of fat than a Happy Hamburger. Find the number of grams of fat in each sandwich if there are a total of 98 grams of fat in the two sandwiches by solving the equation x + (x + 12) = 98 where x represents the number of fat grams in a Happy Hamburger and x + 12 represents the number of fat grams in a Chunky Cheeseburger. x + (x + 12) = 98 2x + 12 = 98 Simplify. 2x = 86 Subtract 12 from both sides. x = 43 Divide both sides by 2. There are 43 fat grams in a Happy Hamburger and 43 + 12 = 55 fat grams in a Chunky Cheeseburger.