What is |((7x-1/3))/(-4)|>= 3/2 ?

The solution to |((7x-1/3))/(-4)|>= 3/2 is x = 19/21

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|((7x-1/3))/(-4)|>= 3/2

\frac{( 7 x - \frac{1}{3} )}{- 4} \geq \frac{3}{2}

x \leq - \frac{17}{21} or x \geq \frac{19}{21}

Interval Notation

(- \infty, - \frac{17}{21}] \cup [\frac{19}{21}, \infty)

Decimal Notation

x \leq - 0.80952 \dots or x \geq 0.90476 \dots

Solution steps

\frac{7 x - \frac{1}{3}}{- 4} \geq \frac{3}{2}

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{7 x - \frac{1}{3}}{- 4} \leq - \frac{3}{2} or \frac{7 x - \frac{1}{3}}{- 4} \geq \frac{3}{2}

\frac{7 x - \frac{1}{3}}{- 4} \leq - \frac{3}{2} or \frac{7 x - \frac{1}{3}}{- 4} \geq \frac{3}{2}

x \leq - \frac{17}{21} or x \geq \frac{19}{21}

∣ 2 x - 1 ∣ + x < 1

4 x^{2} = 35 x + 9

\frac{x ^{9}}{x ^{3}}

2 (x + 4) = 2 x - 4

(6 - 2 i)^{2}

What is |((7x-1/3))/(-4)|>= 3/2 ?
The solution to |((7x-1/3))/(-4)|>= 3/2 is x<=-17/21 \lor x>= 19/21