What is |(4x+9)/(1-2x)|>= 3 ?

The solution to |(4x+9)/(1-2x)|>= 3 is -3/5 <= x< 1/2 \lor 1/2 <x<= 6

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|(4x+9)/(1-2x)|>= 3

\frac{4 x + 9}{1 - 2 x} \geq 3

- \frac{3}{5} \leq x < \frac{1}{2} or \frac{1}{2} < x \leq 6

Solution steps

\frac{4 x + 9}{1 - 2 x} \geq 3

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{4 x + 9}{1 - 2 x} \leq - 3 or \frac{4 x + 9}{1 - 2 x} \geq 3

\frac{4 x + 9}{1 - 2 x} \leq - 3 or \frac{4 x + 9}{1 - 2 x} \geq 3

- \frac{3}{5} \leq x < \frac{1}{2} or \frac{1}{2} < x \leq 6

x + 4 = 3 x

2 x - 4 = x + 6

\frac{3 x}{2} + \frac{2 x}{3} = \frac{1 + 3 x}{2}

\frac{12 x ^{4} y ^{2}}{2 x y ^{5}}

3 t + 1 > 10

What is |(4x+9)/(1-2x)|>= 3 ?
The solution to |(4x+9)/(1-2x)|>= 3 is -3/5 <= x< 1/2 \lor 1/2 <x<= 6