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Popular >

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

Solution

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

Solution

x \leq \frac{2}{3} or x > 2

+2

Interval Notation

(- \infty, \frac{2}{3}] \cup (2, \infty)

Decimal Notation

x \leq 0.66666 \dots or x > 2

Solution steps

\frac{7 x - 2}{2 - x} \leq 2

Rewrite in standard form

\frac{9 x - 6}{2 - x} \leq 0

Factor

\frac{9 x - 6}{2 - x} : \frac{3 ( 3 x - 2 )}{2 - x}

\frac{3 ( 3 x - 2 )}{2 - x} \leq 0

Divide both sides by

3

\frac{\frac{3 ( 3 x - 2 )}{2 - x}}{3} \leq \frac{0}{3}

Simplify

\frac{3 x - 2}{2 - x} \leq 0

Identify the intervals

x \leq \frac{2}{3} or x > 2

Popular Examples

2/((x-1))< 3/((2x-3))

\frac{2}{( x - 1 )} < \frac{3}{( 2 x - 3 )}

3x(x-5)-13>3x^2-2x

3 x (x - 5) - 13 > 3 x^{2} - 2 x

3 x - 10 - 2 x^{2} < 0

\frac{1}{( 3 x - 4 )} < 0

(((x^2-1)(x+2)*(x+1)^2))/((x-2))<0

\frac{( ( x ^{2} - 1 ) ( x + 2 ) \cdot ( x + 1 ) ^{2} )}{( x - 2 )} < 0

Frequently Asked Questions (FAQ)

What is ((7x-2))/((2-x))<= 2 ?
The solution to ((7x-2))/((2-x))<= 2 is x<= 2/3 \lor x>2