Lesson 1.3 Essential Question: How do I solve an equation with variables on both sides of an equal sign. Objective: To solve equations with variables.

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Presentation transcript:

Lesson 1.3 Essential Question: How do I solve an equation with variables on both sides of an equal sign. Objective: To solve equations with variables on both sides of the equal sign Example: 12 + 4x = 10x Subtract 4x from both sides. – 4x – 4x 12 = 6x Divide both sides by 6. 6 6 2 = x Solution Check: 12 + 4(2) = 10(2) 20 = 20

Example: 50 + 9x = 4x Subtract 9x from both sides. – 9x – 9x 50 = – 5x Divide both sides by – 5. – 5 – 5 Solution – 10 = x Check: 50 + 9(-10) = 4(-10) 50 + (-90) = -40 – 40 = – 40

Example: Distribute the 5x – 10 = 3 + 2x Subtract 2x from both sides. – 2x – 2x Add 10 to both sides 3x – 10 = 3 +10 +10 3x = 13 Divide both sides by 3 3 3 x = or

Sometimes an equation does not have only one solution Sometimes an equation does not have only one solution. Some equations have many solutions while others have no solutions. Identity: Is an equation that is true for all values of the variable. (All real numbers are true) Example: 4(x + 2) = 8 + 4x Distribute the 4 4x + 8 = 8 + 4x Subtract 4x from both sides – 4x – 4x True, Therefore this is an identity and all real numbers are solutions 8 = 8 All real numbers To check, Replace x with any number

4 = 7 4 = 7 Example: 9x + 4 = 7 + 9x Subtract 9x from both sides False 4 does not equal 7 therefore there are no solutions. There is no number that will make this true. 4 = 7 No Solution

= + Verbal Models/Problem Solving Example: Hank’s video store charges $8.00 to rent a video game for five days and does not charge an annual membership fee. Bunker’s video only charges $3.00 for a five day rental but has a $50.00 membership fee per year. Find the number of rentals that would cost the same from each store. Hanks Number = Bunkers Number + Membership Charges Rented Charges Rented Fee 8 • x = 3 • x + 50 8x = 3x + 50 Subtract 3x from both sides 5x = 50 Divide both sides by 5 X = 10 If you rent 10 games per year, the cost would be the same.

Review your left column questions. Suggestion: How do you tell the difference between an equation with no solutions and many solutions? Write a summary