What is |(2x-5)/(x-6)|<= 3 ?

The solution to |(2x-5)/(x-6)| = 13

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|(2x-5)/(x-6)|<= 3

\frac{2 x - 5}{x - 6} \leq 3

x \leq \frac{23}{5} or x \geq 13

Interval Notation

(- \infty, \frac{23}{5}] \cup [13, \infty)

Decimal Notation

x \leq 4.6 or x \geq 13

Solution steps

\frac{2 x - 5}{x - 6} \leq 3

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3 \leq \frac{2 x - 5}{x - 6} \leq 3

\frac{2 x - 5}{x - 6} \geq - 3 and \frac{2 x - 5}{x - 6} \leq 3

(x \leq \frac{23}{5} or x > 6) and (x < 6 or x \geq 13)

Merge Overlapping Intervals

x \leq \frac{23}{5} or x \geq 13

10 b^{2} = 27 b + 18

25 w^{6} + 35 w^{3}

\frac{( y - 2 ) ^{2}}{2} = - y + 6

\frac{3 x - 18}{15} = 1 + 2 x

9^{2} + x^{2} = 1 5^{2}

What is |(2x-5)/(x-6)|<= 3 ?
The solution to |(2x-5)/(x-6)|<= 3 is x<= 23/5 \lor x>= 13