3x-5 inequation

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3*x - 5 > 0

3 x - 5 > 0

3*x - 5 > 0

Detail solution

Given the inequality:

3 x - 5 > 0

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

3 x - 5 = 0

Solve:
Given the linear equation:

3*x-5 = 0

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

3 x = 5

Divide both parts of the equation by 3

x = 5 / (3)

x_{1} = \frac{5}{3}

x_{1} = \frac{5}{3}

This roots

x_{1} = \frac{5}{3}

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}{3}

=

\frac{47}{30}

substitute to the expression

3 x - 5 > 0

-5 + \frac{3 \cdot 47}{30} > 0

-3/10 > 0

Then

x < \frac{5}{3}

no execute
the solution of our inequality is:

x > \frac{5}{3}

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Solving inequality on a graph

Rapid solution [src]

And(5/3 < x, x < oo)

\frac{5}{3} < x \wedge x < \infty

(5/3 < x)∧(x < oo)

Rapid solution 2 [src]

(5/3, oo)

x\ in\ \left(\frac{5}{3}, \infty\right)

x in Interval.open(5/3, oo)