Do Now: Solve the following equations. 2. 3. 4. A painting company charges $250 base plus $16 per hour. Another painting company charges $210 base plus $18 per hour. How long is a job for which the two companies costs are the same?

Objective: Students will be able to solve equations to determine the number of solutions.

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Identities and Contradictions WORDS Identity When solving an equation, if you get an equation that is always true, the original equation is an identity, and it has infinitely many solutions. NUMBERS ALGEBRA 2 + 1 = 2 + 1 3 = 3  2 + x = 2 + x –x –x 2 = 2 

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Contradiction When solving an equation, if you get a false equation, the original equation is a contradiction, and it has no solutions. WORDS ALGEBRA NUMBERS Identities and Contradictions 1 = 1 + 2 1 = 3  x = x + 3 –x –x 0 = 3 

Let’s Review….. Steps on solving Multi-Step Equations Lesson 6.2 Equations with Variables on Both Sides Let’s Review….. Steps on solving Multi-Step Equations Don’t call me after midnight 1. D= Distributive property 2. C= combine like term 3. M = move variable to one side 4. A = addition/subtraction 5. M = Multiplication/division

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Example 1: Solve the following equations. Then check your solution. a.)

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Example 1: Solve the following equations. Then check your solution. b.)

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Example 1: Solve the following equations. Then check your solution. c.) d.)

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Example 2: Determine whether the following have one solution, No Solution or infinitely many. If it has one solution, find it. a.)

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Example 2: Determine whether the following have one solution, No Solution or infinitely many. If it has one solution, find it. b.)

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Example 2: Determine whether the following have one solution, No Solution or infinitely many. If it has one solution, find it. c.) d.)

Equations with Variables on Both Sides Lesson 6.2 Equations with Variables on Both Sides Guided Practice: Determine whether the following have one solution, No Solution or infinitely many. If it has one solution, find it. 1.) 2.) 3.) 4x + 16 = 2x 4.) −7x − x + 2 = −8x − 8 2(3x + 2) = 6x + 4 8x – 3 = 15 + 5x