Magnitude Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Solve ∣x∣=6|x| = 6. How many solutions are there?

Solution

  1. 1
    ∣x∣=6|x| = 6 means xx is 6 units from zero on the number line.
  2. 2
    Two points satisfy this: x=6x = 6 (to the right) and x=−6x = -6 (to the left).
  3. 3
    Both solutions: x=6x = 6 or x=−6x = -6.

Answer

x=6 or x=−6x = 6 \text{ or } x = -6
An absolute value equation typically has two solutions because magnitude ignores direction — there is one point 6 units to the right of zero and one 6 units to the left. The only exception is ∣x∣=0|x| = 0, which gives the unique solution x=0x = 0.

About Magnitude

Magnitude measures the size or length of a quantity — for a vector (a, b), it is sqrt(a^2 + b^2). For a single number, magnitude is its absolute value: how far it is from zero, ignoring sign or direction.

Learn more about Magnitude →

More Magnitude Examples

Example 1 easy

Find the magnitude (absolute value) of each: [formula], [formula], [formula].

Example 2 medium

Which has greater magnitude: [formula] or [formula]? Then determine which is greater as a signed num

Example 3 easy

Evaluate [formula].

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