Modulus equations and inequalities
Equations and inequalities · Mathematics
Study notes
Q: Solve (a) |2x - 1| = 5 (b) |x - 3| < 4. (a) 2x - 1 = 5 gives x = 3; 2x - 1 = -5 gives x = -2. Solutions: 3, -2. (b) |x - 3| < 4 means -4 < x - 3 < 4. Add 3: -1 < x < 7. Interval (-1, 7). Check (a): x = 3: |6 - 1| = 5 ✓. x = -2: |-4 - 1| = 5 ✓.