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

The answer to |x-1/2 |=3 2/3 is x=-3 1/6 \lor x=4 1/6

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

The solution is x=-3 1/6 \lor x=4 1/6

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

x = - 3 \frac{1}{6} or x = 4 \frac{1}{6}

Decimal Notation

x = - 3.16666 \dots, x = 4.16666 \dots

Solution steps

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

Convert mixed numbers to improper fractions:

3 \frac{2}{3} = \frac{11}{3}

x - \frac{1}{2} = \frac{11}{3}

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - \frac{1}{2} = - \frac{11}{3} or x - \frac{1}{2} = \frac{11}{3}

x - \frac{1}{2} = - \frac{11}{3} or x - \frac{1}{2} = \frac{11}{3}

x = - \frac{19}{6} or x = \frac{25}{6}

Convert improper fractions to mixed numbers:

\frac{19}{6} = 3 \frac{1}{6}

Convert improper fractions to mixed numbers:

\frac{25}{6} = 4 \frac{1}{6}

x = - 3 \frac{1}{6} or x = 4 \frac{1}{6}

(x - 4)^{2} = 21

5 + 4

2 x^{3} - 6 x

2 x^{2} + 12 x + 15 = 0

64 x^{2} - 1 = 0

What is the answer to |x-1/2 |=3 2/3 ?
The answer to |x-1/2 |=3 2/3 is x=-3 1/6 \lor x=4 1/6
Solve for x: |x-1/2 |=3 2/3
The solution is x=-3 1/6 \lor x=4 1/6