What is |(12-6p)/(p-3)|>= 3p ?

The solution to |(12-6p)/(p-3)|>= 3p is p<= 1\lor (1+sqrt(17))/2 <= p<3\lor 3<p<= 4

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|(12-6p)/(p-3)|>= 3p

\frac{12 - 6 p}{p - 3} \geq 3 p

p \leq 1 or \frac{1 + 17}{2} \leq p < 3 or 3 < p \leq 4

Interval Notation

(- \infty, 1] \cup [\frac{1 + 17}{2}, 3) \cup (3, 4]

Decimal Notation

p \leq 1 or 2.56155 \dots \leq p < 3 or 3 < p \leq 4

Solution steps

\frac{12 - 6 p}{p - 3} \geq 3 p

Find positive and negative intervals

p < 2, 2 \leq p < 3, p \geq 3

Solve the inequality for each interval

p \leq 1 or \frac{1 + 17}{2} \leq p < 3 or 3 < p \leq 4

- 3 + \frac{1}{2}

\frac{6 + 27}{4 - 3}

\frac{5 x - 4}{3} \geq \frac{5}{9}

44 \cdot 5

2 x^{2} - 46 x + 252 = 0

What is |(12-6p)/(p-3)|>= 3p ?
The solution to |(12-6p)/(p-3)|>= 3p is p<= 1\lor (1+sqrt(17))/2 <= p<3\lor 3<p<= 4