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1266 LearnersLast updated on December 2, 2025
Simple Equations And Its Applications
Equations are significant components in mathematics. The equations use the "=" sign to indicate that both sides of an expression are equal. They are widely utilized in finding unknown values. In this topic, we will talk more about simple equations and their applications.
What are Simple Equations?
A simple equation is a mathematical statement that shows the equality of two expressions and contains one variable whose value must be found. It is usually a linear equation in one variable, meaning the variable has a degree of 1.
The simple equations are based on the idea of balance. The equal to sign (=) acts like the center of a weighing scale, where both sides must remain equal. So whatever operation is performed on one side, be it addition, subtraction, multiplication, or division, we must perform the same operation on the other side to keep the equation balanced.
Simple Equation Definition
A simple equation is a linear equation in one variable that shows equality between two expressions and can be solved using basic arithmetic operations to find the value of the unknown variable.
Simple equation example:
Let us consider the simple equation \(2y + 10\).
Here, y is the variable, 2 and 10 are the constants, and + is the operator.
We can solve the equation by keeping both sides balanced:
\(2y + 10 = 12\)
\(2y = 12 - 10\); here, we subtracted 10 from both sides.
\(2y = 2\)
Divide both sides by 2:
\(y = \frac{2}{2}\)
\(y = 1\).
What is Transposition in a Simple Equation?
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 example, 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
\(3p – 3 = 12\)
\(3p = 12 + 3\)
\(3p = 15 \)
\(p = \frac{15}{3}\)
\(p = 5\)
Hence, p is 5.
What is a Linear Equation?
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.
What is the Difference Between Variables and Constants in a Simple Equation?
In simple equations, variables and constants play a vital role. Variables are values that can change, whereas constants are values that remain the same. Let us explore other significant differences between a variable and a constant from the table below:
|
Variables |
Constants |
|---|---|
|
Variables are symbols that represent an unknown value, that may change and are represented commonly using letters like x, y, and z. |
Constants are fixed values that does not change in a simple equation. They are usually any real numbers. |
|
By solving the equation, the value of the variable can be found. |
Constants help to define the equation, but remain the same. |
|
It can be varied depending on the solution of the equation. |
It will not be varied. It will always stay the same. |
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Methods to Solve Simple Equations
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
Trial and Error 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.
| x | LHS (x + 5) | RHS | Is LHS = RHS? |
| 1 | 1 + 5 = 6 | 15 | No |
| 2 | 2 + 5 = 7 | 15 | No |
| 3 | 3 + 5 = 8 | 15 | No |
| 4 | 4 + 5 = 9 | 15 | No |
| 10 | 10 + 5 = 15 | 15 | No |
Therefore, LHS = RHS for x = 10.
Systematic Method
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, \(y = 10\).
Transposition Method
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.
| Adding or subtracting on both sides (systematic method) |
Transposing |
|---|---|
| \(2x – 8 = 4\) Adding 8 to both sides, \(2x – 8 + 8 = 4 + 8\) \(2x = 12\) |
\(2x – 8 = 4\) Transposing –8 from LHS to RHS, (When transposing, –8 becomes +8) \(2x = 12\) |
Therefore, we can apply the transposition method to solve simple equations.
Tips and Tricks to Master Simple Equations
Here are some effective tips and tricks to help in mastering simple equations.
- Simple equations consists of two expressions separated by an equal sign. Your goal is to find the value of the unknown variable that makes both sides equal.
- Perform inverse operations on both sides of the equation, to isolate the variable. This maintains the balance of the equation. For instance, 2y + 10 = 12. Subtract 10: 2y = 2. Now divide by 2: y = 1.
- Move terms from one side of the equation to the other, changing their signs accordingly.
- Practice with trial and error method where substitute different values for the variables, and it helps to find the correct solution.
- Regularly solving a variety of simple equations clarifies the concepts and improves the problem-solving abilities. Practice with worksheets, online resources and problems to build proficiency.
- Parents and teachers can use the balance-scale method while explaining equations. Explain that whatever is done to one side must be done to the other side, to help build a strong foundation in maintaining equality.
- Connect simple equations to real-life situations such as shopping, sharing items equally, or age-based puzzles. This helps them understand why equations matter.
- Parents and teachers can encourage the use of visual aids such as number lines, algebra tiles, or balancing tools in the classroom or at home for hands-on learning.
- Teach a step-by-step method for practicing by having them write each operation clearly below the previous one. This reduces confusion and prevents mistakes among students.
- Help students check answers to simple equations by substituting the found value back into the original equation to see whether both sides are equal.
Common Mistakes and How to Avoid Them in Simple Equations and Its Applications
Simple equations help students find unknown variables easily without complex formulas. However, there are a few common mistakes that students should watch out for. Here’s a list of such mistakes along with steps to avoid them:
Mistake 1
Incorrect Application of Transposition
Sometimes, students might forget to change the sign of terms when they are transposed from one side of the equation to the other.
Example: y - 3 = 21 ⇒ y = 21 + 3
Keep in mind that, when a term is transposed, the sign preceding the term also changes.
Mistake 2
Incorrect Placement of Equal Sign
Students mistakenly misplace equal signs, leading to confusion.
For example: 6a = 12 ⇒ a = 2
Remember that an equal sign should be placed between two equal expressions.
Example: 6a = 12 ⇒ a = 12/6 ⇒ a = 2
Mistake 3
Applying Different Operations on Both Sides
It can be confusing when applying arithmetic operations in an equation. Students might apply different operations on both sides, resulting in incorrect answers.
Ensure that when an arithmetic operation is applied on LHS, the same is applied to the RHS to maintain equality.
Mistake 4
Skipping Steps
While solving the equations, students may directly jump to the answer by skipping steps.
Always write down the solution along with each and every step to avoid miscalculations.
Mistake 5
Confusion between Multiplication and Division
Students might mistakenly divide the terms instead of multiplying them (or vice versa) to isolate the variable.
Example: 5x = 10 ⇒ x = 5/10 (incorrect)
Double-check for errors in inverse operation when transposing terms. Also, ensure that the correct mathematical operation is applied.
Example: 5x = 10 ⇒ x = 10/5 ⇒ x =2
Real World Applications of 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 can be calculated.
- 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.
Solved Examples of Simple Equations and Their Applications
Problem 1
The sum of Roy’s age and his father’s age is 66. If Roy is 20 years old, calculate his father’s age.
Roy’s father is 46 years old.
Explanation
Consider Roy’s father’s age to be y
The equation for the given problem: 20 + y = 66
Now, subtract 20 from both sides,
y = 66 – 20
y = 46
Therefore, Roy’s father is 46 years old.
Problem 2
A teacher asked her students: “If a number is added to 12, the result is 24. Find the number.”
The unknown number is 12.
Explanation
Consider the unknown number as x
The equation for the given problem:
x +12 = 24
We find the value of x by subtracting 12 from both sides:
x = 24 – 12
x = 12
Therefore, the unknown number is 12.
Problem 3
A shopkeeper has 6 boxes of pencils. Each box contains the same number of pencils. If there are 30 pencils in total, how many pencils are in each box?
There are 5 pencils in each box.
Explanation
Consider the number of pencils in each box to be y
6 × x = 30
We find x by dividing both sides by 6:
6 × x = 30 ⇒ x = 30 ÷ 6 ⇒ x = 5
So, there are 5 pencils in each box.
Problem 4
Find the value of x in the equation: 5x – 10 = 40
x = 10.
Explanation
We have:
5x – 10 = 40
To isolate the term with x, we add 10 to both sides:
5x = 50
x = 50/5
x = 10.
Problem 5
Assume a number is subtracted from 60 and the result is 15. Find the number.
The number is 45.
Explanation
Consider the number to be y
The equation for the given problem:
60 – x = 15
Solving for x:
60 - x = 15 ⇒ x = 60 - 15 ⇒ x = 45.
x = 45.
FAQs on Simple Equations and Their Applications
1.What is a simple equation?
2.What is the transposition method?
3.How should I ensure that my solution is correct?
4.Name the three different methods to solve simple equations.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
