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

The answer to |3x-1|+1=1 is x= 1/3

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|3x-1|+1=1

∣ 3 x - 1 ∣ + 1 = 1

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

∣ 3 x - 1 ∣ + 1 = 1

Subtract

1

from both sides

∣ 3 x - 1 ∣ + 1 - 1 = 1 - 1

Simplify

∣ 3 x - 1 ∣ = 0

Apply absolute rule: If

∣ u ∣ = 0

then

u = 0

3 x - 1 = 0

3 x - 1 = 0 : x = \frac{1}{3}

x = \frac{1}{3}

∣ 3 x + 1 ∣ = - 4

\frac{24}{( 4 ( \frac{1}{4} ) + 3 ) ^{\frac{5}{2}}}

(- 4 \frac{1}{2})^{2}

x^{2} - 4 < 5

\frac{5}{7} x + 5 > 10