What is (12)/(x-6)+6/(2x-1)>=-1 ?

The solution to (12)/(x-6)+6/(2x-1)>=-1 is x 6

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

\frac{12}{x - 6} + \frac{6}{2 x - 1} \geq - 1

x \leq - \frac{21}{2} or \frac{1}{2} < x \leq 2 or x > 6

Interval Notation

(- \infty, - \frac{21}{2}] \cup (\frac{1}{2}, 2] \cup (6, \infty)

Decimal Notation

x \leq - 10.5 or 0.5 < x \leq 2 or x > 6

Solution steps

\frac{12}{x - 6} + \frac{6}{2 x - 1} \geq - 1

Rewrite in standard form

\frac{2 x ^{2} + 17 x - 42}{( x - 6 ) ( 2 x - 1 )} \geq 0

Factor

\frac{2 x ^{2} + 17 x - 42}{( x - 6 ) ( 2 x - 1 )} : \frac{( x - 2 ) ( 2 x + 21 )}{( x - 6 ) ( 2 x - 1 )}

\frac{( x - 2 ) ( 2 x + 21 )}{( x - 6 ) ( 2 x - 1 )} \geq 0

Identify the intervals

x \leq - \frac{21}{2} or \frac{1}{2} < x \leq 2 or x > 6

4 ∣ x + 4 ∣ + 6 < 30

4 u - 2 = 14

x^{2} + 2 x y - 24 y^{2}

\frac{40 x ^{8} y ^{8}}{8 x ^{7} y}

3 (2 x + 5) = 39

What is (12)/(x-6)+6/(2x-1)>=-1 ?
The solution to (12)/(x-6)+6/(2x-1)>=-1 is x<=-21/2 \lor 1/2 <x<= 2\lor x>6