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

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

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

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

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

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

Decimal Notation

x = 0.14285 \dots, x = 1

Solution steps

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

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

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

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

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

24 x^{2} - 48 x - 360 = 0

∣ 5 t - 7 ∣ = 11

6 x^{2} + 13 x + 6

6 0^{2} + 6 0^{2} = c^{2}

3 x + 5 = 3 x - 5