Mister Exam
(t-5)(t+4)<0 inequation
The solution
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(t - 5)*(t + 4) < 0
$$\left(t - 5\right) \left(t + 4\right) < 0$$
(t - 5)*(t + 4) < 0
Detail solution
Given the inequality:
$$\left(t - 5\right) \left(t + 4\right) < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(t - 5\right) \left(t + 4\right) = 0$$
Solve:
$$x_{1} = -4$$
$$x_{2} = 5$$
$$x_{1} = -4$$
$$x_{2} = 5$$
This roots
$$x_{1} = -4$$
$$x_{2} = 5$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-4 + - \frac{1}{10}$$
=
$$-4.1$$
substitute to the expression
$$\left(t - 5\right) \left(t + 4\right) < 0$$
$$\left(t - 5\right) \left(t + 4\right) < 0$$
Then
$$x < -4$$
no execute
one of the solutions of our inequality is:
$$x > -4 \wedge x < 5$$
$$\left(t - 5\right) \left(t + 4\right) < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(t - 5\right) \left(t + 4\right) = 0$$
Solve:
$$x_{1} = -4$$
$$x_{2} = 5$$
$$x_{1} = -4$$
$$x_{2} = 5$$
This roots
$$x_{1} = -4$$
$$x_{2} = 5$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-4 + - \frac{1}{10}$$
=
$$-4.1$$
substitute to the expression
$$\left(t - 5\right) \left(t + 4\right) < 0$$
$$\left(t - 5\right) \left(t + 4\right) < 0$$
(-5 + t)*(4 + t) < 0
Then
$$x < -4$$
no execute
one of the solutions of our inequality is:
$$x > -4 \wedge x < 5$$
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