What is the answer to | 1/2 x-2/3 |-1= 1/6 ?

The answer to | 1/2 x-2/3 |-1= 1/6 is x=-1\lor x= 11/3

Solve for x: | 1/2 x-2/3 |-1= 1/6

The solution is x=-1\lor x= 11/3

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\frac{1}{2} x - \frac{2}{3} - 1 = \frac{1}{6}

x = - 1 or x = \frac{11}{3}

Decimal Notation

x = - 1, x = 3.66666 \dots

Solution steps

\frac{1}{2} x - \frac{2}{3} - 1 = \frac{1}{6}

Move

1

to the right side

\frac{1}{2} x - \frac{2}{3} = \frac{7}{6}

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

\frac{1}{2} x - \frac{2}{3} = - \frac{7}{6} or \frac{1}{2} x - \frac{2}{3} = \frac{7}{6}

\frac{1}{2} x - \frac{2}{3} = - \frac{7}{6} or \frac{1}{2} x - \frac{2}{3} = \frac{7}{6}

x = - 1 or x = \frac{11}{3}

∣ x - 3 ∣ + ∣ 3 - x ∣ = 1

∣ x + 1 ∣ = 2 x - 3

∣ - x + 5 ∣ = 8

2 ∣ - 2 x + 5 ∣ = 4

\frac{3 - x}{2} = - 5

What is the answer to | 1/2 x-2/3 |-1= 1/6 ?
The answer to | 1/2 x-2/3 |-1= 1/6 is x=-1\lor x= 11/3
Solve for x: | 1/2 x-2/3 |-1= 1/6
The solution is x=-1\lor x= 11/3