Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 3x+1>-1
- -x^2-6*x*(x^2-1)>0
- (x^2-6*x)/(x^2+6*x+9)<0
- x²-4x-r<0
- Graphing y =:
- 3x+1
- 3x+1
- Integral of d{x}:
-
3x+1
-
-1
- Sum of series:
-
-1
- Derivative of:
-
-1
-
Identical expressions
- 3x+ one >- one
- 3x plus 1 greater than minus 1
- 3x plus one greater than minus one
-
Similar expressions
- sqrt(3*x+1)<=x-1
- 3x+1>+1
- 27^(x+1/3)-10*9^x+10*3^x-5*1/(9^(x+1/2)-10*3^x+3)<=3^x+(1/3)^x-2+(7/3)^(x+1)-1
- 3x-1>-1
- log(1/3)*(x+15)≥log(1/3)(x-1)-2
3x+1>-1 inequation
The solution
Detail solution
Given the inequality:
$$3 x + 1 > -1$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x + 1 = -1$$
Solve:
Given the linear equation:
Move free summands (without x)
from left part to right part, we given:
$$3 x = -2$$
Divide both parts of the equation by 3
$$x_{1} = - \frac{2}{3}$$
$$x_{1} = - \frac{2}{3}$$
This roots
$$x_{1} = - \frac{2}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{2}{3} + - \frac{1}{10}$$
=
$$- \frac{23}{30}$$
substitute to the expression
$$3 x + 1 > -1$$
$$\frac{\left(-23\right) 3}{30} + 1 > -1$$
Then
$$x < - \frac{2}{3}$$
no execute
the solution of our inequality is:
$$x > - \frac{2}{3}$$
$$3 x + 1 > -1$$
To solve this inequality, we must first solve the corresponding equation:
$$3 x + 1 = -1$$
Solve:
Given the linear equation:
3*x+1 = -1
Move free summands (without x)
from left part to right part, we given:
$$3 x = -2$$
Divide both parts of the equation by 3
x = -2 / (3)
$$x_{1} = - \frac{2}{3}$$
$$x_{1} = - \frac{2}{3}$$
This roots
$$x_{1} = - \frac{2}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{2}{3} + - \frac{1}{10}$$
=
$$- \frac{23}{30}$$
substitute to the expression
$$3 x + 1 > -1$$
$$\frac{\left(-23\right) 3}{30} + 1 > -1$$
-13 ---- > -1 10
Then
$$x < - \frac{2}{3}$$
no execute
the solution of our inequality is:
$$x > - \frac{2}{3}$$
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x1
Solving inequality on a graph
Rapid solution
[src]
And(-2/3 < x, x < oo)
$$- \frac{2}{3} < x \wedge x < \infty$$
(-2/3 < x)∧(x < oo)
Rapid solution 2
[src]
(-2/3, oo)
$$x\ in\ \left(- \frac{2}{3}, \infty\right)$$
x in Interval.open(-2/3, oo)