What is (2x(x-4))/(x-1)<= 7 ?

The solution to (2x(x-4))/(x-1)<= 7 is x<= 1/2 \lor 1<x<= 7

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(2x(x-4))/(x-1)<= 7

\frac{2 x ( x - 4 )}{x - 1} \leq 7

x \leq \frac{1}{2} or 1 < x \leq 7

Interval Notation

(- \infty, \frac{1}{2}] \cup (1, 7]

Decimal Notation

x \leq 0.5 or 1 < x \leq 7

Solution steps

\frac{2 x ( x - 4 )}{x - 1} \leq 7

Rewrite in standard form

\frac{2 x ^{2} - 15 x + 7}{x - 1} \leq 0

Factor

\frac{2 x ^{2} - 15 x + 7}{x - 1} : \frac{( 2 x - 1 ) ( x - 7 )}{x - 1}

\frac{( 2 x - 1 ) ( x - 7 )}{x - 1} \leq 0

Identify the intervals

x \leq \frac{1}{2} or 1 < x \leq 7

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What is (2x(x-4))/(x-1)<= 7 ?
The solution to (2x(x-4))/(x-1)<= 7 is x<= 1/2 \lor 1<x<= 7