What is (2x-1)(-5x+10)<= 0 ?

The solution to (2x-1)(-5x+10) = 2

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(2x-1)(-5x+10)<= 0

(2 x - 1) (- 5 x + 10) \leq 0

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

Interval Notation

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

Decimal Notation

x \leq 0.5 or x \geq 2

Solution steps

(2 x - 1) (- 5 x + 10) \leq 0

Rewrite in standard form

- 2 x^{2} + 5 x - 2 \leq 0

Factor

- 2 x^{2} + 5 x - 2 : - (2 x - 1) (x - 2)

- (2 x - 1) (x - 2) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (2 x - 1) (x - 2)) (- 1) \geq 0 \cdot (- 1)

Simplify

(2 x - 1) (x - 2) \geq 0

Identify the intervals

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

\frac{4}{3} \cdot \frac{2}{3}

12 8^{\frac{3}{4}} \cdot 2^{\frac{3}{4}}

\frac{2 x}{3} - x = \frac{x}{15} - \frac{4}{5}

\frac{x}{5} = 9

25 x^{2} - 10 x - 15

What is (2x-1)(-5x+10)<= 0 ?
The solution to (2x-1)(-5x+10)<= 0 is x<= 1/2 \lor x>= 2