What is |(3-5)/((2x-6))|<= 7 ?

The solution to |(3-5)/((2x-6))| = 22/7

Popular >

|(3-5)/((2x-6))|<= 7

\frac{3 - 5}{( 2 x - 6 )} \leq 7

x \leq \frac{20}{7} or x \geq \frac{22}{7}

Interval Notation

(- \infty, \frac{20}{7}] \cup [\frac{22}{7}, \infty)

Decimal Notation

x \leq 2.85714 \dots or x \geq 3.14285 \dots

Solution steps

\frac{3 - 5}{2 x - 6} \leq 7

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 7 \leq \frac{3 - 5}{2 x - 6} \leq 7

\frac{3 - 5}{2 x - 6} \geq - 7 and \frac{3 - 5}{2 x - 6} \leq 7

(x < 3 or x \geq \frac{22}{7}) and (x \leq \frac{20}{7} or x > 3)

Merge Overlapping Intervals

x \leq \frac{20}{7} or x \geq \frac{22}{7}

∣ x - 1 ∣ + ∣ x - 3 ∣ > 2

\frac{( x - 2 )}{( x + 4 )} \leq \frac{( x + 3 )}{( x - 6 )}

∣ x + 3 ∣ + ∣ x - 1 ∣ < ∣ 6 - 3 x ∣

\frac{x ^{2} - 1}{∣ x ^{2} + x + 1 ∣} < 1

x^{2} - 1 \leq 0

What is |(3-5)/((2x-6))|<= 7 ?
The solution to |(3-5)/((2x-6))|<= 7 is x<= 20/7 \lor x>= 22/7