6-5 Solving Open Sentences Involving Absolute Value Objective: Students will be able to solve absolute value equations

What is absolute value? The absolute value of a number is its distance from zero on a number line. Think about this equation. What value(s) of x would make the equation true. {-3, 3}

In most instances, absolute value equations are going to contain two solutions, as seen in the previous problem. Think about this problem. Can you determine what the solutions would be? {-2, 6} How about this one: {-10, 4} Examining the last couple examples, can you think of algebraic steps to follow when solving absolute value equations?

Steps for solving absolute value equations Isolate the absolute value term on one side of the equation, and all other terms on the other side of the equation, so that you attain an equation that looks like: 2) Set up and solve two equations. a) For the first equation, drop the absolute value symbol and solve. b) For the second equation, drop the absolute value symbol and make “b” negative. Then solve.

Let’s walk through an example together. Solve

Directions: Solve each absolute value equation. 1) 2)

3) 4) Remember, absolute value can never be negative 3) 4) Remember, absolute value can never be negative! There is no such thing as negative distance.

Try these. 5) 6) 7)

Solve each absolute value equation. 8) 9)

10) Try this. 11)

12) 13)

14)

Try these. 15) 16)