What is 3/(4-x)<= 6/(1-x) ?

The solution to 3/(4-x)<= 6/(1-x) is x<1\lor 4<x<= 7

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3/(4-x)<= 6/(1-x)

\frac{3}{4 - x} \leq \frac{6}{1 - x}

x < 1 or 4 < x \leq 7

Interval Notation

(- \infty, 1) \cup (4, 7]

Solution steps

\frac{3}{4 - x} \leq \frac{6}{1 - x}

Rewrite in standard form

\frac{3 x - 21}{( - x + 4 ) ( - x + 1 )} \leq 0

Factor

\frac{3 x - 21}{( - x + 4 ) ( - x + 1 )} : \frac{3 ( x - 7 )}{( - x + 4 ) ( - x + 1 )}

\frac{3 ( x - 7 )}{( - x + 4 ) ( - x + 1 )} \leq 0

Divide both sides by

3

\frac{\frac{3 ( x - 7 )}{( - x + 4 ) ( - x + 1 )}}{3} \leq \frac{0}{3}

Simplify

\frac{x - 7}{( - x + 4 ) ( - x + 1 )} \leq 0

Identify the intervals

x < 1 or 4 < x \leq 7

\frac{1}{3 - 1}

17 x - 3 < 4 x - 9

3 x^{2} + 12 x + 8 = 0

3 z + 18 = 2 z + 6

What is 3/(4-x)<= 6/(1-x) ?
The solution to 3/(4-x)<= 6/(1-x) is x<1\lor 4<x<= 7