What is (5-6/4 x)/(1/2 x-3)-5/6 <= 6+2x^0 ?

The solution to (5-6/4 x)/(1/2 x-3)-5/6 6

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(5-6/4 x)/(1/2 x-3)-5/6 <= 6+2x^0

\frac{5 - \frac{6}{4} x}{\frac{1}{2} x - 3} - \frac{5}{6} \leq 6 + 2 x^{0}

x \leq \frac{378}{71} or x > 6

Interval Notation

(- \infty, \frac{378}{71}] \cup (6, \infty)

Decimal Notation

x \leq 5.32394 \dots or x > 6

Solution steps

\frac{5 - \frac{6}{4} x}{\frac{1}{2} x - 3} - \frac{5}{6} \leq 6 + 2 x^{0}

Rewrite in standard form

\frac{- 71 x + 378}{x - 6} \leq 0

Identify the intervals

x \leq \frac{378}{71} or x > 6

4 x^{2} + 8 x + 4 = 4

y - 10 \leq 14

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

2 b + (- 7) = - 21

3 x^{2} + 5 x - 4 = 0

What is (5-6/4 x)/(1/2 x-3)-5/6 <= 6+2x^0 ?
The solution to (5-6/4 x)/(1/2 x-3)-5/6 <= 6+2x^0 is x<= 378/71 \lor x>6