a) |x| = 2
x = 2 ∨ -x = 2
x = 2 ∨ x = -2
x ∈ {-2, 2}
b) |1/2x| = -4
1/2x = -4 ∨ -1/2x = -4
x = -8 ∨ x = 8
x ∈ {-8, 8}
c) |x + 2| = 2
x + 2 = 2 ∨ -x - 2 = 2
x = 0 ∨ -x = 4
x = 0 ∨ x = -4
x ∈ {-4, 0}
d) |x - 3| < 2
x - 3 < 2 ∨ -x + 3 < 2
x < 5 ∨ -x < -1
x < 5 ∨ x > 1
x ∈ (1, 5)
e) |x - 1| ≥ 2
x - 1 ≥ 2 ∨ -x + 1 ≥ 2
x ≥ 3 ∨ -x ≥ 1
x ≥ 3 ∨ x ≤ -1
x ∈ (-∞, -1> ∨ <3, ∞+)
f) |5x + 1| > 1/5
5x + 1 > 1/5 ∨ -5x - 1 > 1/5
5x > -4/5 ∨ -5x > 6/5
x > -4/25 ∨ x < -6/25
x ∈ (-∞, [tex]-\frac{6}{25}[/tex]) ∨ ([tex]-\frac{4}{25}[/tex], ∞+)
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