What is ((6-2x))/(2x+3)<= 0 ?

The solution to ((6-2x))/(2x+3) = 3

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((6-2x))/(2x+3)<= 0

\frac{( 6 - 2 x )}{2 x + 3} \leq 0

x < - \frac{3}{2} or x \geq 3

Interval Notation

Decimal

x < - 1.5 or x \geq 3

Solution steps

\frac{6 - 2 x}{2 x + 3} \leq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( x - 3 ) ) ( - 1 )}{2 x + 3} \geq 0 \cdot (- 1)

Simplify

\frac{2 ( x - 3 )}{2 x + 3} \geq 0

Divide both sides by

2

\frac{\frac{2 ( x - 3 )}{2 x + 3}}{2} \geq \frac{0}{2}

Simplify

\frac{x - 3}{2 x + 3} \geq 0

Identify the intervals

x < - \frac{3}{2} or x \geq 3

\frac{4 a ^{2} b ^{5}}{2 a ^{6} b ^{2}}

\frac{x}{5} - \frac{x}{8} = \frac{3}{4}

(x + 3)^{2} - 4 = 0

25 x^{2} - 5 x - 20

- 2 a (a + b - 5) + 3 (- 5 a + 2 b) + b (6 a + b - 8)

What is ((6-2x))/(2x+3)<= 0 ?
The solution to ((6-2x))/(2x+3)<= 0 is x<-3/2 \lor x>= 3