What is |(x+3)/(6-3x)|<= 2 ?

The solution to |(x+3)/(6-3x)| = 3

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|(x+3)/(6-3x)|<= 2

\frac{x + 3}{6 - 3 x} \leq 2

x \leq \frac{9}{7} or x \geq 3

Interval Notation

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

Decimal Notation

x \leq 1.28571 \dots or x \geq 3

Solution steps

\frac{x + 3}{6 - 3 x} \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq \frac{x + 3}{6 - 3 x} \leq 2

\frac{x + 3}{6 - 3 x} \geq - 2 and \frac{x + 3}{6 - 3 x} \leq 2

(x < 2 or x \geq 3) and (x \leq \frac{9}{7} or x > 2)

Merge Overlapping Intervals

x \leq \frac{9}{7} or x \geq 3

\frac{2}{11} (\frac{11}{2})

ln (0.8)

6 x^{2} - 8 x = 0

3 x^{2} - 14 x - 5 = 0

∣ - x + 3 ∣ - x - 4 = 0

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