What is -x-4<= 6/(x-3)<= x-4 ?

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-x-4<= 6/(x-3)<= x-4

- x - 4 \leq \frac{6}{x - 3} \leq x - 4

1 \leq x \leq 2 or x \geq 6

Solution steps

- x - 4 \leq \frac{6}{x - 3} \leq x - 4

a \leq u \leq b

then

a \leq u and u \leq b

- x - 4 \leq \frac{6}{x - 3} and \frac{6}{x - 3} \leq x - 4

- x - 4 \leq \frac{6}{x - 3} : - 3 \leq x \leq 2 or x > 3

\frac{6}{x - 3} \leq x - 4 : 1 \leq x < 3 or x \geq 6

Combine the intervals

(- 3 \leq x \leq 2 or x > 3) and (1 \leq x < 3 or x \geq 6)

Merge Overlapping Intervals

1 \leq x \leq 2 or x \geq 6

\frac{t}{\frac{5}{12}} = - \frac{3}{10}

4 π + \frac{π}{2}

2.3 \cdot (2.3 - 4.3) + 4.3 \cdot (4.3 - 2.3)

P (r, s) = r - s - 4

\frac{1}{12 a - 3} - \frac{16 a ^{2}}{12 a - 3}

What is -x-4<= 6/(x-3)<= x-4 ?
The solution to -x-4<= 6/(x-3)<= x-4 is 1<= x<= 2\lor x>= 6