What is ((5x-8))/((x-3))>= 3 ?

The solution to ((5x-8))/((x-3))>= 3 is x 3

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((5x-8))/((x-3))>= 3

\frac{( 5 x - 8 )}{( x - 3 )} \geq 3

x \leq - \frac{1}{2} or x > 3

Interval Notation

(- \infty, - \frac{1}{2}] \cup (3, \infty)

Decimal Notation

x \leq - 0.5 or x > 3

Solution steps

\frac{5 x - 8}{x - 3} \geq 3

Rewrite in standard form

\frac{2 x + 1}{x - 3} \geq 0

Identify the intervals

x \leq - \frac{1}{2} or x > 3

5 x - 3 x^{2} > 0

(x + 1)^{2} + 3 > 0

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

x \cdot (x - 1)^{2} \leq 0

(3 x - 1) (- 2 x + 4) < 0

What is ((5x-8))/((x-3))>= 3 ?
The solution to ((5x-8))/((x-3))>= 3 is x<=-1/2 \lor x>3