In this lesson, students learn how to solve basic equations involving absolute values. They first use the connection between absolute value and distance on a number line to reason about a solution. Then, students recall the piecewise definition of absolute value to rewrite an absolute value equation into two linear equations that give the solutions.
Solve equations by reasoning about distance on a number line.
Use the piecewise definition of absolute value to solve equations.
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Identify the effect on the graph of replacing by , , , and for specific values of (both positive and negative); find the value of given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.