Mister Exam
4+2t/3.<3 inequation
The solution
Detail solution
Given the inequality:
$$\frac{2 t}{3} + 4 < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 t}{3} + 4 = 3$$
Solve:
Given the linear equation:
Move free summands (without t)
from left part to right part, we given:
$$\frac{2 t}{3} = -1$$
Divide both parts of the equation by 2/3
$$t_{1} = - \frac{3}{2}$$
$$t_{1} = - \frac{3}{2}$$
This roots
$$t_{1} = - \frac{3}{2}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$t_{0} < t_{1}$$
For example, let's take the point
$$t_{0} = t_{1} - \frac{1}{10}$$
=
$$- \frac{3}{2} + - \frac{1}{10}$$
=
$$- \frac{8}{5}$$
substitute to the expression
$$\frac{2 t}{3} + 4 < 3$$
$$\frac{\left(- \frac{8}{5}\right) 2}{3} + 4 < 3$$
the solution of our inequality is:
$$t < - \frac{3}{2}$$
$$\frac{2 t}{3} + 4 < 3$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 t}{3} + 4 = 3$$
Solve:
Given the linear equation:
4+2*t/3 = 3
Move free summands (without t)
from left part to right part, we given:
$$\frac{2 t}{3} = -1$$
Divide both parts of the equation by 2/3
t = -1 / (2/3)
$$t_{1} = - \frac{3}{2}$$
$$t_{1} = - \frac{3}{2}$$
This roots
$$t_{1} = - \frac{3}{2}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$t_{0} < t_{1}$$
For example, let's take the point
$$t_{0} = t_{1} - \frac{1}{10}$$
=
$$- \frac{3}{2} + - \frac{1}{10}$$
=
$$- \frac{8}{5}$$
substitute to the expression
$$\frac{2 t}{3} + 4 < 3$$
$$\frac{\left(- \frac{8}{5}\right) 2}{3} + 4 < 3$$
44 -- < 3 15
the solution of our inequality is:
$$t < - \frac{3}{2}$$
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t1
Solving inequality on a graph
Rapid solution
[src]
And(-oo < t, t < -3/2)
$$-\infty < t \wedge t < - \frac{3}{2}$$
(-oo < t)∧(t < -3/2)
Rapid solution 2
[src]
(-oo, -3/2)
$$t\ in\ \left(-\infty, - \frac{3}{2}\right)$$
t in Interval.open(-oo, -3/2)