What is 4/x+3/(x-2)<= 1 ?

The solution to 4/x+3/(x-2) = 8

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4/x+3/(x-2)<= 1

\frac{4}{x} + \frac{3}{x - 2} \leq 1

x < 0 or 1 \leq x < 2 or x \geq 8

Interval Notation

(- \infty, 0) \cup [1, 2) \cup [8, \infty)

Solution steps

\frac{4}{x} + \frac{3}{x - 2} \leq 1

Rewrite in standard form

\frac{- x ^{2} + 9 x - 8}{x ( x - 2 )} \leq 0

Factor

\frac{- x ^{2} + 9 x - 8}{x ( x - 2 )} : \frac{- ( x - 1 ) ( x - 8 )}{x ( x - 2 )}

\frac{- ( x - 1 ) ( x - 8 )}{x ( x - 2 )} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 1 ) ( x - 8 ) ) ( - 1 )}{x ( x - 2 )} \geq 0 \cdot (- 1)

Simplify

\frac{( x - 1 ) ( x - 8 )}{x ( x - 2 )} \geq 0

Identify the intervals

x < 0 or 1 \leq x < 2 or x \geq 8

3 c^{2} - 7 c

5 x^{2} - 18 x + 16 = 0

\frac{x - 3}{x + 5} > 0

\frac{3 x - 5}{x - 2} \geq \frac{4}{x + 1}

2 x^{2} - 2 x

What is 4/x+3/(x-2)<= 1 ?
The solution to 4/x+3/(x-2)<= 1 is x<0\lor 1<= x<2\lor x>= 8