What is (5x-8)/(x-1)>= (7x-4)/(x+2) ?

The solution to (5x-8)/(x-1)>= (7x-4)/(x+2) is -2<x<1\lor 5/2 <= x<= 4

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(5x-8)/(x-1)>= (7x-4)/(x+2)

\frac{5 x - 8}{x - 1} \geq \frac{7 x - 4}{x + 2}

- 2 < x < 1 or \frac{5}{2} \leq x \leq 4

Interval Notation

(- 2, 1) \cup [\frac{5}{2}, 4]

Decimal Notation

- 2 < x < 1 or 2.5 \leq x \leq 4

Solution steps

\frac{5 x - 8}{x - 1} \geq \frac{7 x - 4}{x + 2}

Rewrite in standard form

\frac{- 2 x ^{2} + 13 x - 20}{( x - 1 ) ( x + 2 )} \geq 0

Factor

\frac{- 2 x ^{2} + 13 x - 20}{( x - 1 ) ( x + 2 )} : \frac{- ( 2 x - 5 ) ( x - 4 )}{( x - 1 ) ( x + 2 )}

\frac{- ( 2 x - 5 ) ( x - 4 )}{( x - 1 ) ( x + 2 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 2 x - 5 ) ( x - 4 ) ) ( - 1 )}{( x - 1 ) ( x + 2 )} \leq 0 \cdot (- 1)

Simplify

\frac{( 2 x - 5 ) ( x - 4 )}{( x - 1 ) ( x + 2 )} \leq 0

Identify the intervals

- 2 < x < 1 or \frac{5}{2} \leq x \leq 4

\frac{4}{3} π

24 (4 t + 1.4)^{2} - 79 (4 t + 1.4) + 20 = 15543

3 x + 1 = 5

x^{2} + 19 x + 60 = 0

8 - 13 x + 5 x^{2}

What is (5x-8)/(x-1)>= (7x-4)/(x+2) ?
The solution to (5x-8)/(x-1)>= (7x-4)/(x+2) is -2<x<1\lor 5/2 <= x<= 4