Absolute Value Inequalities Math Example 4

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

Example 4

hard
Solve โˆฃ3x+6โˆฃ>0|3x + 6| > 0.

Solution

  1. 1
    โˆฃ3x+6โˆฃ>0|3x + 6| > 0 whenever 3x+6โ‰ 03x + 6 \neq 0, i.e., xโ‰ โˆ’2x \neq -2.
  2. 2
    Solution: all real numbers except x=โˆ’2x = -2.

Answer

xโ‰ โˆ’2x \neq -2
Absolute value is zero only when the expression inside is zero. It is positive for all other values.

About Absolute Value Inequalities

Absolute value inequalities describe values within or outside a fixed distance from a center.

Learn more about Absolute Value Inequalities โ†’

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