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Absolute Value Equations

Discover what absolute value is, its symbol, and how to solve equations involving absolute value. Learn the key concept of distance from zero and practice isolating the absolute value.

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Absolute Value Equations

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  1. Absolute Value Equations

  2. What is absolute value? Absolute value is the distance a point is away from zero on the number line. It is also sometimes called magnitude.

  3. What is absolute value? There are 2 points for every given distance (except for zero) one in the positive direction and one in the negative direction.

  4. | | The symbol for absolute value is two vertical lines | |. Be careful that you don’t confuse them with parentheses, which are curvy ( )

  5. | 5 | The absolute value of + 5: | + 5 | = 5 because the point + 5 is 5 units away from zero on the number line.

  6. | - 5 | The absolute value of – 5: | - 5 | = 5 because the point - 5 is 5 units away from zero on the number line.

  7. The meaning of absolute value How many numbers are 5 units away from zero on the number line? | x | = 5 There are 2 answers: both + 5 and - 5

  8. Solve this equation! | x + 2| = 5 | stuffing| = 5 Stuffing can either equal + 5 or – 5 x + 2 = +5 | x + 2 = – 5 x = + 5 – 2| x = – 5 – 2 x = 3| x = -7

  9. FIRST: Isolate the Absolute Value | x + 2|+ 7 = 15 | x + 2| = 15 – 7 |stuffing|= 8 Stuffing can either equal + 8 or – 8 x + 2 = +8 | x + 2 = – 8 x = + 8 – 2 | x = – 8 – 2 x = 6 | x = – 10

  10. Trick question | x + 2|+ 7 = 5 | x + 2| = 5 – 7 |stuffing|= – 2 Whoa! Absolute value can never be negative! Answer is “No Solution”

  11. Absolute Value Means distance from zero or “magnitude” Always positive or zero since it is a distance. Absolute value equations – isolate the absolute value Solve for both + and – on the right Expect 2 answers.

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