What is 1/2 |3x+2/3 |> 5/6 ?

The solution to 1/2 |3x+2/3 |> 5/6 is x 1/3

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1/2 |3x+2/3 |> 5/6

\frac{1}{2} 3 x + \frac{2}{3} > \frac{5}{6}

x < - \frac{7}{9} or x > \frac{1}{3}

Interval Notation

(- \infty, - \frac{7}{9}) \cup (\frac{1}{3}, \infty)

Decimal Notation

x < - 0.77777 \dots or x > 0.33333 \dots

Solution steps

\frac{1}{2} 3 x + \frac{2}{3} > \frac{5}{6}

Multiply both sides by

2

3 x + \frac{2}{3} > \frac{5}{3}

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

u > a

3 x + \frac{2}{3} < - \frac{5}{3} or 3 x + \frac{2}{3} > \frac{5}{3}

3 x + \frac{2}{3} < - \frac{5}{3} or 3 x + \frac{2}{3} > \frac{5}{3}

x < - \frac{7}{9} or x > \frac{1}{3}

2 y + 2 = 16

10 t - 24 = 21 - 10 t

- 5 (x - 1) \geq 10

\frac{2}{3 - 2}

\frac{x}{2} - 12 = - 14

What is 1/2 |3x+2/3 |> 5/6 ?
The solution to 1/2 |3x+2/3 |> 5/6 is x<-7/9 \lor x> 1/3