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Chapter 2 Discovery 1 Linear Equations with Noninteger Solutions (5 x 4) 2(3x 1) 2( x 7) does not have an integer solution. Complete the table of values, compare the values obtained, and determine their differences. x 3 (5 x 4) 2(3x 1) 2( x 7) 8 1 1 8 1 (8) 7 4 5 6 7 Write a rule for determining when the solution of an equation is between two integers given in a table of values. Chapter 2 Discovery 2 Linear Equations with No Solution 1. Solve 2 x 5 2 x 10 numerically by completing a table of values. Write a rule explaining how to solve the equation by viewing its table of values. 2. Solve 2 x 5 2 x 10 graphically. Sketch the graph. Write a rule explaining how to solve the equation by viewing its graph. Chapter 2 Discovery 3 Linear Equation with Many Solutions 1. Solve 2 x 5 ( x 3) ( x 2) numerically by completing a table of values. Write a rule explaining how to solve the equation by viewing its table of values. 2. Solve 2 x 5 ( x 3) ( x 2) graphically. Sketch the graph. Write a rule explaining how to solve the equation by viewing its graph. Chapter 2 Discovery 4 Linear Equation with No Solutions Solve algebraically the previous example of a linear equation with no solution: 2 x 5 2 x 10 Write a rule that explains why the equation has no solution. Chapter 2 Discovery 5 Linear Equation with Many Solutions Solve algebraically the previous example of a linear equation with many solutions: 2x + 5 = (x + 3) + (x + 2). Write a rule that explains why the equation has many solutions. Chapter 2 Discovery 6 Solving a Linear Absolute-Value Equation Solve each equation graphically and check your solution numerically. 1. a. x4 3 2. a. x 4 3 3. a. x4 0 b. 3 x 2 b. 3 x 2 b. x 3 0 Write a rule that gives the number of solutions of a linear absolute-value equation when the absolute-value expression equals a positive number, a negative number, and 0.