What is the answer to | 1/x-3|=4 ?

The answer to | 1/x-3|=4 is x=-1\lor x= 1/7

Solve for x: | 1/x-3|=4

The solution is x=-1\lor x= 1/7

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\frac{1}{x} - 3 = 4

x = - 1 or x = \frac{1}{7}

Decimal Notation

x = - 1, x = 0.14285 \dots

Solution steps

\frac{1}{x} - 3 = 4

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

\frac{1}{x} - 3 = - 4 or \frac{1}{x} - 3 = 4

\frac{1}{x} - 3 = - 4 or \frac{1}{x} - 3 = 4

x = - 1 or x = \frac{1}{7}

∣ 6 x - 2 ∣ = - 4

x^{2} - 4 x - 5 = 5

- 4 ∣ 5 - 2 n ∣ = - 12

3 ∣ 2 x - 5 ∣ - 4 = - 1

∣ - 3 n - 4 ∣ = 17