What is |(x+3)/(2x)|<= 10 ?

The solution to |(x+3)/(2x)| = 3/19

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|(x+3)/(2x)|<= 10

\frac{x + 3}{2 x} \leq 10

x \leq - \frac{1}{7} or x \geq \frac{3}{19}

Interval Notation

(- \infty, - \frac{1}{7}] \cup [\frac{3}{19}, \infty)

Decimal Notation

x \leq - 0.14285 \dots or x \geq 0.15789 \dots

Solution steps

\frac{x + 3}{2 x} \leq 10

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 10 \leq \frac{x + 3}{2 x} \leq 10

\frac{x + 3}{2 x} \geq - 10 and \frac{x + 3}{2 x} \leq 10

(x \leq - \frac{1}{7} or x > 0) and (x < 0 or x \geq \frac{3}{19})

Merge Overlapping Intervals

x \leq - \frac{1}{7} or x \geq \frac{3}{19}

lo g_{3} (0)

(- \frac{8}{27})^{- \frac{4}{3}}

8 x^{2} - 2 x - 2

16 x^{2} - 14 x

5 a^{2} - 6 a

What is |(x+3)/(2x)|<= 10 ?
The solution to |(x+3)/(2x)|<= 10 is x<=-1/7 \lor x>= 3/19