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Popular >

(x-8)/(4-x)>= 5

Solution

\frac{x - 8}{4 - x} \geq 5

Solution

4 < x \leq \frac{14}{3}

+2

Interval Notation

(4, \frac{14}{3}]

Decimal Notation

4 < x \leq 4.66666 \dots

Solution steps

\frac{x - 8}{4 - x} \geq 5

Rewrite in standard form

\frac{6 x - 28}{4 - x} \geq 0

Factor

\frac{6 x - 28}{4 - x} : \frac{2 ( 3 x - 14 )}{4 - x}

\frac{2 ( 3 x - 14 )}{4 - x} \geq 0

Divide both sides by

2

\frac{\frac{2 ( 3 x - 14 )}{4 - x}}{2} \geq \frac{0}{2}

Simplify

\frac{3 x - 14}{4 - x} \geq 0

Identify the intervals

4 < x \leq \frac{14}{3}

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8 x^{2} + 10 x - 3 = 0

Frequently Asked Questions (FAQ)

What is (x-8)/(4-x)>= 5 ?
The solution to (x-8)/(4-x)>= 5 is 4<x<= 14/3