What is (|x+5|)/(x^2-6x+8)<= 2 ?

The solution to (|x+5|)/(x^2-6x+8)<= 2 is x=-5\lor 2<x<4

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(|x+5|)/(x^2-6x+8)<= 2

\frac{∣ x + 5 ∣}{x ^{2} - 6 x + 8} \leq 2

x = - 5 or 2 < x < 4

Solution steps

\frac{∣ x + 5 ∣}{x ^{2} - 6 x + 8} \leq 2

Move

2

to the left side

\frac{∣ x + 5 ∣}{x ^{2} - 6 x + 8} - 2 \leq 0

∣ x + 5 ∣ \geq 0

\frac{a}{b} \leq 0 and a \geq 0

then

b < 0 or a = 0

x^{2} - 6 x + 8 < 0 or ∣ x + 5 ∣ = 0

x^{2} - 6 x + 8 < 0 : 2 < x < 4

∣ x + 5 ∣ = 0 : x = - 5

Combine the intervals

2 < x < 4 or x = - 5

Merge Overlapping Intervals

x = - 5 or 2 < x < 4

81 x^{2} = 4

(0.903 \cdot 200) + (70 \cdot 4.179) = t (0.903 + 4.179)

\frac{3}{4} f + 5 = - 5

(5 m^{2} - 3 m^{2} + 6) (- 3 m + 2)

6 w^{2} + 24 w = 0

What is (|x+5|)/(x^2-6x+8)<= 2 ?
The solution to (|x+5|)/(x^2-6x+8)<= 2 is x=-5\lor 2<x<4