√ Definition of One Variable Linear Inequality (PtLSV), Properties, Examples of Problems and How to Solve them
Definition of One Variable Linear Inequality (PtLSV), Properties, Examples of Problems and How to Solve them – In this discussion we will explain about one-variable linear inequalities. Which includes the notion of one-variable linear inequality, the properties of one-variable linear inequality, examples of questions and ways to solve one-variable linear inequalities with complete and easy discussion understandable. For more details, please see the review below carefully.
Definition of One Variable Linear Inequality (PtLSV), Properties, Examples of Problems and How to Solve them
Let's discuss the definition first carefully.
Definition of One Variable Linear Inequality (PtLSV)
One-variable linear inequalities are open sentences that have only one variable and degree one and contain the relationship ( > or < ). Look at the following sentences:
- X > 6
- 3x – 3 < 8
- 3b > b+6
- 5n – 3 < 3n + 2
Open sentences above use hyphens , > or <. This sentence is called an inequality.
“Each of these inequalities has only one variable, namely x, a and n. This inequality is called a one-variable inequality. The inequality variable (variable) above is raised to the first power or is also called first degree, so it is called linear inequality.
The general form of PtLSV in variables can be expressed as follows:
ax + b < 0, ax + b > 0, or ax + b > 0, or ax + b < 0, with a < 0, a and b real (real) numbers
Below are some examples of PtLSV with variable x.
- 3x – 2 < 0
- 3x – 2 < 0
- 5x – 1 > 8
- 3x + 1 > 2x – 4
- 10 < 2(x + 1)
Properties of One Variable Linear Inequality
As is the case with one-variable linear equations, in determining the solution to one-variable linear inequalities can be done by means of substitution.
However, this can also be done by subtracting, adding, multiplying, or dividing both sides of the inequality by the same number. Like A < B one variable linear inequality x and C are nonzero constants.
The inequality A < B is equivalent to:
- A + C < B + C
- A – C < B – C
- A x C < B x C, if C > 0 for all x
- A x C > B x C, if C < 0 for all x
- A/C < B/C, if C > 0 for all x
- A/C > B/C, if C < 0 for all x
The properties above also apply to the symbol ">" or "<”
Examples of PtLSV Problems and How to Solve them
Below are examples of questions and how to solve them and also answers to one-variable linear inequalities.
1. Addition and Subtraction
Please note the inequalities below:
x + 3 < 8, where x is a variable of an integer.
For:
x = 1, so 1 + 3 < 8, is true
x = 2, so 2 + 3 < 8, is true
x = 3, so 3 + 3 < 8, is true
x = 4, so 4 + 3 < 8, is false
Substitutes for x are 1,2, and 3 so that the inequality x + 3 < 8 is true is called a solution of the inequality.
Example:
Find the solution of 4x > 3x – 5, for:
2. Multiplication or division
Look at the inequalities below:
For natural x numbers less than 10, the solution is x = 7, x = 8, or x = 9
Based on the description above, it can be concluded that:
"Every inequality remains equivalent, with the sign of the inequality unchanged, even though both sides are multiplied by the same positive number"
Problems example:
Now consider the following inequalities:
a. –x > – 5, where x is a natural number less than 8. The satisfactory substitutes for x are x = 1, x = 2, x = 3 or x = 4.
Another way to solve the inequality above is to multiply both sides by the same negative number.
* –x > –5
–1(–x) > –1(–5), (both sides multiplied by –1 and constant inequality sign)
x > 5
The solution is x = 6 or x = 7.
* –x > –5
–1(–x) < –1(–5), (both sides are multiplied by –1 and the inequality sign changes from > to
x < 5
The solution is x = 1, x = 2, x = 3, or x = 4.
Based on the solution, it turns out that the inequality has the same solution, namely
–x > –5 and –1(–x) < –1(–5)
so, –x > –5 <=> –1(–x) < –1(–5)
b. –4x <–8, where x is a natural number less than 4. A satisfactory substitute for x is x = 2, or x = 3. so, the solution is x = 2 or x = 3.
Based on the explanation above it can be concluded that:
"An inequality when both sides are multiplied by the same negative number then the sign of the inequality changes"
Example:
Thus has been explained about Definition of One Variable Linear Inequality (PtLSV), Properties, Examples of Problems and How to Solve them, hopefully can add to your insight and knowledge. Thank you for visiting and don't forget to read other articles.
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