What is |(x+1)/(3x+5)|<= 1 ?

The solution to |(x+1)/(3x+5)| =-3/2

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|(x+1)/(3x+5)|<= 1

\frac{x + 1}{3 x + 5} \leq 1

x \leq - 2 or x \geq - \frac{3}{2}

Interval Notation

(- \infty, - 2] \cup [- \frac{3}{2}, \infty)

Decimal Notation

x \leq - 2 or x \geq - 1.5

Solution steps

\frac{x + 1}{3 x + 5} \leq 1

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 1 \leq \frac{x + 1}{3 x + 5} \leq 1

\frac{x + 1}{3 x + 5} \geq - 1 and \frac{x + 1}{3 x + 5} \leq 1

(x < - \frac{5}{3} or x \geq - \frac{3}{2}) and (x \leq - 2 or x > - \frac{5}{3})

Merge Overlapping Intervals

x \leq - 2 or x \geq - \frac{3}{2}

(2 + 3 i)^{2} - (3 i - 6) = 1 + 9 i

x^{3} + 7 x^{2} - 2 x - 14

6 x^{2} - 7 x - 49 = 0

5 x^{2} - 12 x + 8 = 5

3 - \frac{4 x}{5} = 2

What is |(x+1)/(3x+5)|<= 1 ?
The solution to |(x+1)/(3x+5)|<= 1 is x<=-2\lor x>=-3/2