Write the distributed expression. Activating Prior Knowledge Notes Tie to LO M4:LSN7 Classifying Solutions to Linear Equations Learning Objective Today, we will classify solutions to linear equations. CFU M4:LSN2 Linear and Non-Linear Expressions in x CFU Concept Development Review Notes #1 & 2 1. Constants are fixed numbers. 2. When a term is the product of a constant(s) and a power of x, the constant is called a coefficient. M4:LSN7 Classifying Solutions to Linear Equations CFU Concept Development Pair Share unique solution M4:LSN7 Classifying Solutions to Linear Equations CFU Concept Development Pair Share no solution M4:LSN7 Classifying Solutions to Linear Equations CFU Concept Development Pair Share infinitely many solutions M4:LSN7 CFU Concept Development Notes #3 Solve the following equations we will review in about 5 minutes. 7x 3 = 7x + 5 7x 3 = 5x + 5 Classifying Solutions to Linear Equations 7x 3 = x M4:LSN7 CFU Concept Development Look at Notes #3 Classifying Solutions to Linear Equations 7x 3 = 5x + 57x 3 = 7x + 57x 3 = x 7x 3 = 5x x 2x 3 = x = 8 2 x = 4 What does x = 4 mean for the equation 7x 3 = 5x + 5 ? How many solutions make this equation true? M4:LSN7 CFU Concept Development Look at Notes #3 Classifying Solutions to Linear Equations 7x 3 = 5x + 57x 3 = 7x + 57x 3 = x 7x 3 = 5x + 5 What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? M4:LSN7 CFU Concept Development Look at Notes #3 Classifying Solutions to Linear Equations 7x 3 = 5x + 57x 3 = 7x + 57x 3 = x 7x 3 = 7x x 3 = 5 Does -3 = 5? What does this mean about the equation 7x 3 = 7x + 5 ? M4:LSN7 CFU Concept Development Look at Notes #3 Classifying Solutions to Linear Equations 7x 3 = 5x + 57x 3 = 7x + 57x 3 = x 7x 3 = 7x + 5 What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? M4:LSN7 CFU Concept Development Look at Notes #3 Classifying Solutions to Linear Equations 7x 3 = 5x + 57x 3 = 7x + 57x 3 = x -7x 3 = -3 What value makes 7x 3 = x true? Does -3 = -3? 7x 3 = x 7x 3 = 7x - 3 What do you notice about this equation? M4:LSN7 CFU Concept Development Look at Notes #3 Classifying Solutions to Linear Equations 7x 3 = 5x + 57x 3 = 7x + 57x 3 = x What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? M4:LSN7 CFU Concept Development Notes #4 Classifying Solutions to Linear Equations What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? 3x + 4 = 8x - 96x + 5 = 8 + 6x10x 4 = x -4x 5 = 6 11x12 15x = -2 15x-2x + 5 = -2x x = 9x + 7 Generalize about the equations unique solution, no solution, or infinitely many solutions. **2 minutes ** M4:LSN7 CFU Skill Development/Guided Practice Notes #5 Classifying Solutions to Linear Equations What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. Concept Development Whiteboard Complete the following equation so that it doesnt have a solution. Classifying Solutions to Linear Equations M4:LSN7 CFU 3x + 1 = ___________ M4:LSN7 CFU Skill Development/Guided Practice Notes #6 Classifying Solutions to Linear Equations 8 9x = 15x x What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. 8 9x = 18x + 7 Concept Development Whiteboard Complete the following equation so that it has infinitely many solutions. Classifying Solutions to Linear Equations M4:LSN7 CFU 3x + 1 = ___________ M4:LSN7 CFU Skill Development/Guided Practice Notes #7 Classifying Solutions to Linear Equations 5(x + 9) = 5x + 45 What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. 5x + 45 = 5x + 45 Concept Development Whiteboard Complete the following equation so that it has only one solution. Classifying Solutions to Linear Equations M4:LSN7 CFU 3x + 1 = ___________ M4:LSN7 CFU Skill Development/Guided Practice Notes #8 Classifying Solutions to Linear Equations -3x + 32 7x = -2(5x + 10) What do you notice about the coefficients in the equation? What do you notice about the constants in the equation? Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the equation into a simpler form if necessary. -10x + 32 = -10x - 20 1. What did we learn today? Closure Complete at the end of notes 2. Why is this important to you? 3. How can you tell if an equation has infinitely many solutions? CFU