Lesson 5: 2-5 Solving Equations Involving Absolute Value

What are the two cases you must consider when solving an absolute value equation?

When does an absolute value equation have no solution? Why?

When does an absolute value equation have only one solution?

solve an equation
equivalent equations
linear equation

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

A.REI.1 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.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

3A Functions
3B Functions
3C Functions

The absolute value of a number is the distance the number is from zero on the number line. To solve an equation involving absolute value, first isolate the absolute value on one side of the equation and rewrite the equation as a compound sentence using the word or. The solution set of an absolute value equation can be graphed on a number line or written in set notation.

The average January temperature in a northern Canadian city is 1°F. The actual January temperature for that city may be about 5°F warmer or colder. Write and solve an equation to find the maximum and minimum temperatures.

Error Analysis: In Exercise 63, suggest that students consider why Wesley thinks the solution set is the empty set. Students should see that the absolute value is equal to a negative number. Since absolute value represents the distance from zero on a number line and distance cannot be a negative number, there is no solution.

If students are having trouble rewriting absolute value equations, then have them apply the two situations (positive and negative) to the expression within the absolute value symbols. For example, |x| = 4 can be written as x = 4 or as -x = 4, which yields x = -4.

Practice: Exercises 1 - 12

Exercises 65 - 74

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