10x^2-25x>0 — step-by-step solution

1) Let's solve in

ℝ

10 x^{2} - 25 x > 0

You can factorize the expression:

10 x^{2} - 25 x

into:

x \cdot (10 x - 25)

We study the sign of each factor of the product

⇥The expression

x

is zero at

x = 0

, it is negative before and positive after

⇥The expression

10 x - 25

is zero at:

⇥

x = \frac{25}{10}

⇥ⓘ We simplify the fraction by dividing the numerator and the denominator by

5

, their greatest common divisor:

\frac{25}{10}

\frac{5 \cdot 5}{2 \cdot 5}

\frac{5}{2}

⇥

x = \frac{5}{2}

⇥Its coefficient of

x

10

, being positive, it is negative before and positive after

\frac{5}{2}

2) Let's draw up the sign table:

▶Solution obtained:

x \in (-∞, 0) \cup (\frac{5}{2}, +∞)

3) The numeric value of:

x \in (-∞, 0) \cup (\frac{5}{2}, +∞)

is:

▷

x \in (-∞, 0) \cup (2.5, +∞)