What is (2x+1)/(3x-6)>= 3 ?

The solution to (2x+1)/(3x-6)>= 3 is 2<x<= 19/7

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(2x+1)/(3x-6)>= 3

\frac{2 x + 1}{3 x - 6} \geq 3

2 < x \leq \frac{19}{7}

Interval Notation

(2, \frac{19}{7}]

Decimal Notation

2 < x \leq 2.71428 \dots

Solution steps

\frac{2 x + 1}{3 x - 6} \geq 3

Rewrite in standard form

\frac{- 7 x + 19}{3 x - 6} \geq 0

Factor

\frac{- 7 x + 19}{3 x - 6} : \frac{- 7 x + 19}{3 ( x - 2 )}

\frac{- 7 x + 19}{3 ( x - 2 )} \geq 0

Multiply both sides by

3

\frac{3 ( - 7 x + 19 )}{3 ( x - 2 )} \geq 0 \cdot 3

Simplify

\frac{- 7 x + 19}{x - 2} \geq 0

Identify the intervals

2 < x \leq \frac{19}{7}

\frac{12 a ^{2} + 54 a}{54 a}

(45 - 3 x) \frac{1}{2} = x - 9

12 x y + 10 y - 18 x - 15

y - 7 y + 6 = 30

5 x - 17 > 8