Absolute Value Equations

Learn and apply absolute value equations using equations, examples, and interpretation.

Lesson 3 of 53 parts Practice Flashcards

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Absolute Value as Distance

Objective: Explain and use absolute value as distance in an Algebra 1 problem.

The value |x−c| is the distance of x from c on a number line and is never negative. Distance cannot be negative.

Worked examples

Try itExample 1.1: How many real solutions does |x−5|=3?Show answer

2. A positive distance has one point on each side of the center. The answer is 2.

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Absolute Value as Distance

Objective: Explain and use absolute value as distance in an Algebra 1 problem.

The value |x−c| is the distance of x from c on a number line and is never negative. Distance cannot be negative.

Worked examples

Try itExample 1.1: How many real solutions does |x−5|=3?Show answer

2. A positive distance has one point on each side of the center. The answer is 2.

Two-Branch Equations

Objective: Explain and use two-branch equations in an Algebra 1 problem.

For d>0, |x−c|=d means x−c=d or x−c=−d; both candidate answers must be checked. When the specified distance is zero.

Worked examples

Try itExample 2.1: How many real solutions does |x−8|=4?Show answer

2. A positive distance has one point on each side of the center. The answer is 2.

Extraneous or Impossible Cases

Objective: Explain and use extraneous or impossible cases in an Algebra 1 problem.

Absolute value equal to a negative number has no real solution; domain restrictions may also exclude a candidate branch. Transformations or restrictions may invalidate a candidate.

Worked examples

Try itExample 3.1: How many real solutions does |x−11|=2?Show answer

2. A positive distance has one point on each side of the center. The answer is 2.

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