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Absolute value equations

Level 8 · Algebra 2 · for questions like “Solve |2x − 4| = 6.”

💡 The idea

|something| = 6 means the something is 6 or −6. So there are usually two answers.

🪜 The steps

  1. Split it: 2x − 4 = 6 or 2x − 4 = −6.
  2. Solve each one.

✏️ Worked examples

1. |2x − 4| = 6: 2x = 10 gives x = 5, and 2x = −2 gives x = −1. So x = 5 or x = −1.

2. |x + 3| = 7: x = 4 or x = −10.

⚠️ Watch out

🎯 Try these

  1. |x − 2| = 5
  2. |3x + 3| = 12
  3. |x + 1| = 4

Answers: 1) 7 or −3 2) 3 or −5 3) 3 or −5

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