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Absolute Value Equations

Form: |ax + b| = c

Condition: c ≥ 0

Solution: |ax + b| = c ⟺ ax + b = c or ax + b = -c

|x| = 5

Form: |ax + b| = |cx + d|

Solution: Consider two cases:

  • ax + b = cx + d
  • ax + b = -(cx + d)
|x| = |x - 2|

Left side: |ax + b|

Right side: |cx + d|

Form: |ax + b| + |cx + d| = e

Solution: Create a sign table and solve for each interval

|x + 1| + |x - 2| = 5