√ Definition of One Variable Linear Equation (PLSV) & Example Problems
Definition of One Variable Linear Equation (PLSV) & Example Problems – In this discussion, we will explain about one-variable linear equations. Which includes the understanding of the meaning of one-variable linear equations and examples of one-variable equation problems with complete and easy discussion. To find out more details, please see the review below carefully.
Definition of One Variable Linear Equation (PLSV) & Example Problems
Let's discuss the meaning of PLSV first carefully.
Definition of One Variable Linear Equation (PLSV)
Linear Equation One Variable is an opening sentence that is connected with an equal sign ( = ) and has only one exponential variable 1. The general form of a one-variable linear equation is ax + b = 0. Examples of one-variable linear equations include:
x + 4 – 8
3a + 5 = 16
6b – 2 = 18x, a, and b are variables (variables) that can be replaced with any satisfying number.
Example of Solving One Variable Linear Equation
There are two ways to determine the solution and set of solutions to a one-variable linear equation, namely:
- Substitution
- Look for equivalent equations
The equation can be expressed in an equivalent equation, namely by:
a. Add or subtract two sides with the same number
b. Multiply or divide on both sides by the same non-zero number
According to the explanation above, in order to better understand, we give an example as follows:
It is known that the equation 3x – 1 = 14; if x is a member of the set P = (3, 4, 5, 6)!
Answer:
3x-1+14 x Є P = (3,4,5,6)
a. Substitution way:
3x-1= 14; if x = 3 = then 3(3) – 1 = 8 (false)
3x-1= 14; if x = 4 = then 3(4) – 1 = 11 (false)
3x-1= 14; if x = 5 = then 3(5) – 1 = 14 (true)
3x-1= 14; if x = 6 = then 3(6) – 1 = 17 (false)
So the solution to 3x -1 = 14 is 5
b. Finding equivalent equations
From the table above, if x = 5, substitute in (a), (b), and (c) so that the equation becomes an equality.
(a).
3x-1=14
3(5) – 1 = 14
14 = 14 (equivalent)
(b).
3x = 15
3 (5) = 15
15 = 15 (equivalent)
(c).
x = 5
5 = 5 (equivalent)
Which means 3x – 1 = 14 and 3x = 15 are equivalent equations.
Example of a One Variable Linear Equation Problem and its Discussion
1. Mr. Agus owns a piece of land that is rectangular in shape, the width of the land he owns is 5 meters shorter than the length. The circumference of Pak Sugeng's land is 50 meters. Then calculate the length and width of Pak Agus' land!
How to Solve it:
Given: The circumference of the land = 50m
For example, the length of the land = x, then the width of the land = x-5
The perimeter of the land = the perimeter of the rectangle
50 = 2 (p + l)
50 = 2 ( x + x – 5)
50 = 2 (2x – 5)
50 = 4x – 10
50 + 10 = 4x
60 = 4x
60:4 = x
15 = x
So that
Land length: x = 15 meters
Land width: x-5 = 15-5 = 10 meters
So, the length of Pak Agus' land is 15 meters and the width of the land is 10 meters.
2. The x value that satisfies the equation 4x + 6 = 18 is
How to solve:
4x + 6 = 18
4x = 18-6
4x = 12
x = 12:4
x = 3
3. For the equation 4x + y = 12, if x = -1 then what is y?
How to solve:
4( -1) + y = 12
-4 + y = 12
y = 12 + 4
y = 16
4. It is known that the sum of three even numbers in sequence is 66. Determine the smallest number!
How to solve:
Given: Three even numbers add up to 66
Even numbers have a pattern + 2, for example the first even number = x, then the second and third even numbers respectively = x+2, and x+4, so:
Number.1 + Number.2 + Number.3 = 66
x + (x+2) + (x+4) = 66
3x + 6 = 66
3x = 60
x=20
So that
The first even number is: x = 20
The second even number is x+2 = 20+2 = 22
The third even number is x+4 = 20+4 = 24
5. The value of x that satisfies the equation 5x-7 = 3x+5, namely?
How to solve:
5x- 7 = 3x + 5
5x – 3x = 5 + 7
2x = 12
x = 6
Thus has been explained about Definition of One Variable Linear Equation (PLSV) & Example Problemshopefully can add to your insight and knowledge. Thank you for visiting and don't forget to read other articles.
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