x-3x+5>0 inequation

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x - 3*x + 5 > 0

\left(- 3 x + x\right) + 5 > 0

-3*x + x + 5 > 0

Detail solution

Given the inequality:

\left(- 3 x + x\right) + 5 > 0

To solve this inequality, we must first solve the corresponding equation:

\left(- 3 x + x\right) + 5 = 0

Solve:
Given the linear equation:

x-3*x+5 = 0

Looking for similar summands in the left part:

5 - 2*x = 0

Move free summands (without x)
from left part to right part, we given:

- 2 x = -5

Divide both parts of the equation by -2

x = -5 / (-2)

x_{1} = \frac{5}{2}

x_{1} = \frac{5}{2}

This roots

x_{1} = \frac{5}{2}

is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:

x_{0} < x_{1}

For example, let's take the point

x_{0} = x_{1} - \frac{1}{10}

=

- \frac{1}{10} + \frac{5}{2}

=

\frac{12}{5}

substitute to the expression

\left(- 3 x + x\right) + 5 > 0

\left(\frac{12}{5} - \frac{3 \cdot 12}{5}\right) + 5 > 0

1/5 > 0

the solution of our inequality is:

x < \frac{5}{2}

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Solving inequality on a graph

Rapid solution 2 [src]

(-oo, 5/2)

x\ in\ \left(-\infty, \frac{5}{2}\right)

x in Interval.open(-oo, 5/2)

Rapid solution [src]

And(-oo < x, x < 5/2)

-\infty < x \wedge x < \frac{5}{2}

(-oo < x)∧(x < 5/2)