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

The solution to 1/((3x-2))<= 1/((3x+4)) is -4/3 <x< 2/3

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1/((3x-2))<= 1/((3x+4))

\frac{1}{( 3 x - 2 )} \leq \frac{1}{( 3 x + 4 )}

- \frac{4}{3} < x < \frac{2}{3}

Interval Notation

(- \frac{4}{3}, \frac{2}{3})

Decimal Notation

- 1.33333 \dots < x < 0.66666 \dots

Solution steps

\frac{1}{3 x - 2} \leq \frac{1}{3 x + 4}

Rewrite in standard form

\frac{1}{( 3 x - 2 ) ( 3 x + 4 )} \leq 0

\frac{1}{a} \leq 0

then

a < 0

(3 x - 2) (3 x + 4) < 0

Identify the intervals

- \frac{4}{3} < x < \frac{2}{3}

n^{5} - n^{3} < 0

\frac{( ( x - 1 ) ^{2} \cdot ( x + 1 ) ^{3} )}{( x ^{4} \cdot ( x - 2 ) )} < 0

\frac{3 \cdot ( 1 - x )}{2 + 2 x - 1} > \frac{3 x - 1}{2}

1 \geq \frac{3}{( 3 - 2 x - x ^{2} )}

x^{2} + 3 x + 1 < 0

What is 1/((3x-2))<= 1/((3x+4)) ?
The solution to 1/((3x-2))<= 1/((3x+4)) is -4/3 <x< 2/3