What is |(x^2-4x)/(x^2+x+2)|<= 1 ?

The solution to |(x^2-4x)/(x^2+x+2)| =-2/5

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|(x^2-4x)/(x^2+x+2)|<= 1

\frac{x ^{2} - 4 x}{x ^{2} + x + 2} \leq 1

x \geq - \frac{2}{5}

Solution steps

\frac{x ^{2} - 4 x}{x ^{2} + x + 2} \leq 1

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 1 \leq \frac{x ^{2} - 4 x}{x ^{2} + x + 2} \leq 1

\frac{x ^{2} - 4 x}{x ^{2} + x + 2} \geq - 1 and \frac{x ^{2} - 4 x}{x ^{2} + x + 2} \leq 1

True for all x and x \geq - \frac{2}{5}

Merge Overlapping Intervals

x \geq - \frac{2}{5}

3 + d < 3 - d

(7 - 5) (21 - 15)

3 p \geq - 24

36 - 25 x^{2}

(2 x - 3)^{3}

What is |(x^2-4x)/(x^2+x+2)|<= 1 ?
The solution to |(x^2-4x)/(x^2+x+2)|<= 1 is x>=-2/5