What is (X+1)/(2X-4)< 1/(1/3 X-1) ?

The solution to (X+1)/(2X-4)< 1/(1/3 X-1) is 4-sqrt(7)<X<2\lor 3<X<4+sqrt(7)

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(X+1)/(2X-4)< 1/(1/3 X-1)

\frac{X + 1}{2 X - 4} < \frac{1}{\frac{1}{3} X - 1}

4 - 7 < X < 2 or 3 < X < 4 + 7

Interval Notation

(4 - 7, 2) \cup (3, 4 + 7)

Decimal Notation

1.35424 \dots < X < 2 or 3 < X < 6.64575 \dots

Solution steps

\frac{X + 1}{2 X - 4} < \frac{1}{\frac{1}{3} X - 1}

Rewrite in standard form

\frac{X ^{2} - 8 X + 9}{( X - 2 ) ( X - 3 )} < 0

Factor

X^{2} - 8 X + 9 : (X - 4 - 7) (X - 4 + 7)

\frac{( X - 4 - 7 ) ( X - 4 + 7 )}{( X - 2 ) ( X - 3 )} < 0

Identify the intervals

4 - 7 < X < 2 or 3 < X < 4 + 7

x^{2} + 36

2 x - 3 \leq 1

2 (x - 4)^{2} = 2

7 a + 28 b

lo g_{2} (4096)

What is (X+1)/(2X-4)< 1/(1/3 X-1) ?
The solution to (X+1)/(2X-4)< 1/(1/3 X-1) is 4-sqrt(7)<X<2\lor 3<X<4+sqrt(7)