Simple Equations And Its Applications

Simple equations are mathematical statements with an equal sign and at least one unknown quantity (variable) to solve for. As the term suggests, they are straightforward and can be solved without the use of complex methods. 

For example: 2y +10 = 12 is a simple equation where y is the variable.

 
Here, we apply arithmetic operations to find the value of y

2y + 10 = 12

2y = 12 – 10

2y = 2

y = 1

The transposition method involves shifting terms across the equal sign while changing their signs accordingly. For example, positive becomes negative and vice-versa. Also, arithmetic operations change when transposing terms.

For e.g., addition becomes subtraction, and division becomes multiplication (and vice versa). This technique helps us in finding the unknown variable by isolating it.

Take a look at this example for better understanding:

Find the value of p

3p – 3 = 12

3p = 12 + 3

3p = 15 

p = 15/3

p = 5

Hence, p is 5.

A linear equation is another term for a simple equation that involves one or more variables. Solving linear equations is straightforward and can be done using simple methods like graphing. Linear equations can also be solved by transposing the terms or by balancing the LHS and RHS. 

Note that, when a number is transposed, its preceding sign changes.

For example:  

Prove LHS = RHS for 8x + y = 24, given x = 2 and y = 8

8 (2) + 8 = 24

16 + 8 = 24

24 = 24

Therefore, LHS = RHS.

Solving simple equations determines the values of the unknown variable in the given equation. In a simple equation, the LHS and RHS should be equivalent. There are different methods for solving simple equations, as mentioned below:
 

• Trial and error method
   
• Systematic method
   
• Transposition method

In a trial and error method, we substitute random values for the variable to check if it satisfies the equation LHS = RHS.

For example: x + 5 = 15

Where:

LHS = x + 5

RHS = 15

Let’s now perform the trial and error method by substituting values starting from 1 to check if LHS = RHS.
 

Therefore, LHS = RHS for x = 10

The systematic method also known as the balance method is used to balance the equation by performing the mathematical operations on both sides of the equation. This systematic approach compares both sides of the equation to a weighing balance. It maintains equality by adding or removing values from each side of the equation.

For example: y – 2 = 8

We add 2 to both sides to isolate y 

y – 2 + 2 = 8 + 2

Thus, y = 10.

The transposition method simplifies the equation by shifting terms across the equal sign. Below is a table exhibiting both systematic and transposition methods for the same equation.
 

Therefore, we can apply the transposition method to solve simple equations.

Simple equations are widely used in problem-solving in various real-life situations. They are used in different fields beyond mathematics. Let’s look into some:
 

• Simple equations help families make financial plans each month. For example, if you save $500 per week, how long will it take to save $10,000?
   
• By solving the problems involving simple equations, children can enhance their problem-solving abilities.
   
• Workers can use these equations to calculate their wages easily. For example, if a person earns $300 per day, how much can they earn in 20 days? Using the equation y = 300 × 20, we can determine the total earnings. Solution y = $6000.
   
• Students can apply simple linear equations when solving problems related to measurements, speed, distance, and time.
   
• Learning simple equations helps us to easily determine the final price of an item after a discount.