What is (x-1/2)(2x^2-2x-12)>= 0 ?

The solution to (x-1/2)(2x^2-2x-12)>= 0 is -2 = 3

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(x-1/2)(2x^2-2x-12)>= 0

(x - \frac{1}{2}) (2 x^{2} - 2 x - 12) \geq 0

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

Interval Notation

[- 2, \frac{1}{2}] \cup [3, \infty)

Decimal Notation

- 2 \leq x \leq 0.5 or x \geq 3

Solution steps

(x - \frac{1}{2}) (2 x^{2} - 2 x - 12) \geq 0

Factor

(x - \frac{1}{2}) (2 x^{2} - 2 x - 12) : 2 (x + 2) (x - 3) (x - \frac{1}{2})

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

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

\frac{- 8 n + 4}{11 n ( n + 1 )} \cdot \frac{4 n ^{2}}{- 10 n + 5}

9 w^{2} + 9 w - 4

(- \frac{5}{6})^{2}

(- 49)^{\frac{1}{2}}

(\frac{6}{5})^{2}

What is (x-1/2)(2x^2-2x-12)>= 0 ?
The solution to (x-1/2)(2x^2-2x-12)>= 0 is -2<= x<= 1/2 \lor x>= 3