What is the answer to |2z-1|=4 ?

The answer to |2z-1|=4 is z=-3/2 \lor z= 5/2

Solve for z: |2z-1|=4

The solution is z=-3/2 \lor z= 5/2

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∣ 2 z - 1 ∣ = 4

z = - \frac{3}{2} or z = \frac{5}{2}

Solution steps

∣ 2 z - 1 ∣ = 4

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

2 z - 1 = - 4 or 2 z - 1 = 4

2 z - 1 = - 4 or 2 z - 1 = 4

z = - \frac{3}{2} or z = \frac{5}{2}

∣ 5 x + 9 ∣ = x

3 ∣ 2 k - 8 ∣ + 3 = 69

∣ 2 z + 64 ∣ = 8

∣ 13 x + 12 ∣ = 19

- 3 ∣ p ∣ = - 3