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Simple Equations and Its Applications
Equations are one of the most important aspects of Mathematics. The word determines the equality between the two sides of an equation. It makes sure both the expressions of the equation are equal by using the simple sign of ‘equal to’ (=). Equations help in balancing out the expressions from both the sides with the use of the arithmetic operations like addition, subtraction, division and multiplication. To understand this concept completely we need to understand the use of constants and variables.
|1.||Introduction to Simple Equations|
|2.||Transposition or Transposing|
|3.||Application of Simple Equations|
|7.||FAQs on Simple Equations and Its Applications|
Introduction to Simple Equations
A mathematical equation that represents the relationship between two expressions on either side of the equal sign (=) is a Simple Equation. An equation consists of variables and numerical constants. For example, x + 4 = 10 where x is a variable. The numbers 4 and 10 are constants, as they do not change. + is an operator, the operator may be + or –
In the above equation, we aim to find the value of x. Once the value is determined, the equation x + 4 has to be equal to 10. Even if the Left Hand Side (LHS) is interchanged with the Right Hand Side (RHS), the equation will remain the same. A simple equation remains unchanged if the same number is added, subtracted, and multiplied to each side of the equation and divided by the same non-zero number.
Transposition or Transposing
One of the applications of simple equations is to solve the equation by shifting the variable or the number to the other side of the ‘=’ sign. However, we have to keep in mind that the sign preceding the number changes as well. For instance, ‘+’ becomes ‘-’ and ‘-’ becomes ‘+’ when the sides are changed. But for division and multiplication it different, multiplication transported will go as division, and division transported will go as multiplication.
For example : Find the value of x
3x - 5 = 10
3x = 10 + 5
3x = 15
x = 15/ 3
x = 5
Therefore, the value of x is 5
Application of Simple Equations
Simple equations can be used to solve problems in real-life situations as well. The application of simple equations depends on the situation wherein we need to form the equation ourselves and find the value of the unknown variable. We face such situations while purchasing items at a shop, calculating age problems, finding the missing numbers, guessing the unknown numbers and calculating the speed or time of the train and so on. We translate the situations in the form of equations. We develop strategies in the form of equations to solve these problems. For example, if a child wants to purchase 10 pencils and a box that together cost $35, the cost of one pencil can be assumed as x and the cost of one box can be assumed as y and the equation could be acquired as 10x + y = 35.
Simple equations and its applications can be seen in different mathematical concepts as well such as in Algebra, Geometry, and Fractions. Algebra and Geometry are one of the most important chapters for children. Simple equations and its applications help in understanding the concept of algebra in an early phase.
Simple equations can also be called Linear Equations where there is more than one variable and can be solved by using different methods such as using a graph, balancing the equation by making LHS = RHS, and by transposing. To solve a linear equation it will be helpful to know how to transpose or rearrange formulas. When solving a linear equation we try to make the unknown quantity the subject of the equation.
For example: 4x + y = 11 with values of x and y being 2 and 3 respectively.
4(2) + 3 = 11
8 + 3 = 11
11 = 11
Therefore, LHS = RHS
- Equations can have one or two variables but the simplest way to solve is by balancing the equation and transposing the numbers.
- While transposing the numbers the preceding signs of the number change.
- While balancing the equation, the number should be the same on both sides.
- The application of simple equations are used in our everyday life and can be solved easily.
Example 1: Prove that LHS = RHS in this equation x + 4 = 10
Solution: x + 4 = 10
x + 4 - 4 = 10 - 4
x = 6
The value of X is 6 and when X is replaced with the value in the equation we get
6 + 4 = 10
Therefore, LHS = RHS
Example 2: In an isosceles triangle, the vertex angle is 40 degrees. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180 degrees)
In an isosceles triangle, the base angles are equal.
Let the base angles be of x degrees each.
The Sum of three angles of a triangle is 180
40 + x + x = 180
40 + 2x = 180
Now, transposing 40 will make it -40.
2x = 180 - 40
2x = 140
Now again transposing 2, will make it /2
x = 140/2
x = 70
Thus the base angles are 70 degrees each.
Example 3: If your mother gives you Rs.100 to go buy apples and says keep Rs.40 from it to buy chocolates and you find out the price of one kg of apples is Rs.12, so how many apples should you buy for everyone?
Let us assume that you have to buy apples in Kg, so the total amount of money that you will be spending is Rs. 12x. Now, you have Rs.40 for yourself. So the equation will be?
12x + 40 = 100
(transposing 40 to the other side i.e. it becomes ‘- 40’)
12x = 100 - 40
12x = 60
x = 60/12
x = 5
Therefore, you can buy 5 kgs of Apples and buy chocolates.
FAQs on Simple Equations and its Applications
What is a Simple Equation?
A simple equation refers to a mathematical equation that balances the relationship between both the LHS and RHS with an ‘equal to’ sign. This category of an equation consists of a variable, usually in the form of x and y.
Why is Transposition Required?
Solving simple equations often require rearranging them. In such cases, a variable ‘X’ needs to be introduced on one side of the equation along with the constants mentioned on the other side. This method is known as the process of transposition. Any mathematical operation like addition, subtraction, multiplication, and division performed on one side of the equation requires to be done on the other side as well. It is essential to balance the equation with both sides being equal to each other.
What is a Variable?
Variable means an unknown factor in an equation that a simple equation aims to find out. An equation can also have multiple variables in which case it will be known as the quadratic equation. Variables play different roles in different mathematical formulas. It can be identified via various specific names such as an indeterminate variable, which appears in a formal power series.
What is the Example of a Simple Equation?
An example of a simple equation is 4x - 15 = 25. The letter that is used to substitute for numbers in algebra is known as a variable. However, there are certain letters and symbols that substitute for a fixed value in a simple equation and these are knowns as constants.
What is a Constant?
A Constant is the fixed number in an equation that is rearranged to find the value of the variables x and y. These numbers do not change but by using arithmetic operations like addition, subtraction, multiplication, and division, these constants are rearranged and calculated.
What is the Difference Between a Simple Equation and a Linear Equation?
A mathematical equation which has a mathematical expression on both side along with at least one variable and an equal sign (=) is known as a simple equation. eg. 5x+3x = 8x
Whereas, a mathematical equation which has a mathematical expression on both side along with two variables and an equal sign (=) is known as a linear equation. eg x = 3y +6