What is 1<((3x^2-7x+8))/((x^2+1))<= 2 ?

The solution to 1<((3x^2-7x+8))/((x^2+1))<= 2 is 1<= x<= 6

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1<((3x^2-7x+8))/((x^2+1))<= 2

1 < \frac{( 3 x ^{2} - 7 x + 8 )}{( x ^{2} + 1 )} \leq 2

1 \leq x \leq 6

Interval Notation

[1, 6]

Solution steps

1 < \frac{( 3 x ^{2} - 7 x + 8 )}{( x ^{2} + 1 )} \leq 2

a < u \leq b

then

a < u and u \leq b

1 < \frac{( 3 x ^{2} - 7 x + 8 )}{( x ^{2} + 1 )} and \frac{( 3 x ^{2} - 7 x + 8 )}{( x ^{2} + 1 )} \leq 2

1 < \frac{3 x ^{2} - 7 x + 8}{x ^{2} + 1} :

True for all

x

\frac{3 x ^{2} - 7 x + 8}{x ^{2} + 1} \leq 2 : 1 \leq x \leq 6

Combine the intervals

True for all x and 1 \leq x \leq 6

Merge Overlapping Intervals

1 \leq x \leq 6

1 < x < 5

- 1 < \frac{( 5 - x )}{3} \leq 7

3 \leq ∣ x - 4 ∣ \leq 8

- 4 \leq 5 - x < 2

- 3 < 4 - 7 \frac{x}{2} < 18

What is 1<((3x^2-7x+8))/((x^2+1))<= 2 ?
The solution to 1<((3x^2-7x+8))/((x^2+1))<= 2 is 1<= x<= 6