Class 7 — Mathematics (NCERT)
Simple Equations
Class 7
- ✓By the end of this lesson students will be able to understand what an equation is.
- ✓By the end of this lesson students will be able to form simple equations from given statements.
- ✓By the end of this lesson students will be able to solve simple linear equations in one variable using various methods.
- ✓By the end of this lesson students will be able to apply simple equations to solve real-life problems.
Key concepts
An equation is a condition on a variable. It states that two expressions are equal. It always contains an equality sign (=). For example, x + 5 = 12 is an equation, where the expression on the L.H.S. (x + 5) is equal to the expression on the R.H.S. (12).
A variable is a symbol, usually a letter (like x, y, z, p, m, n, etc.), used to represent an unknown quantity. Its value is not fixed and can change.
A constant is a value that does not change. It has a fixed numerical value. For example, in the equation x + 5 = 12, the numbers 5 and 12 are constants.
To solve an equation means to find the value of the variable that makes the equation true. In the balancing method, we perform the same mathematical operation (addition, subtraction, multiplication, or division) on both sides of the equation to isolate the variable, thus maintaining the balance of the equation.
Transposing means moving a term from one side of the equation to the other. When a term is transposed, its sign changes. For example, if a term is added on one side, it becomes subtracted on the other side when transposed. This is a quicker way to apply the balancing method.
Setting up an equation involves translating a verbal statement or a word problem into a mathematical equation. This requires identifying the unknown quantity, assigning a variable to it, and then representing the relationships described in the statement using mathematical operations (+, -, ×, ÷) and an equality sign.
Key facts to remember
- 1An equation always contains an equality sign (=).
- 2The L.H.S. of an equation must be equal to its R.H.S. for the equation to be true.
- 3A variable represents an unknown quantity whose value we need to find.
- 4To solve an equation, we find the value of the variable that satisfies the equation.
- 5You can add, subtract, multiply, or divide the same non-zero number on both sides of an equation without changing its solution.
- 6When transposing a term from one side of the equation to the other, its sign must be changed.
- 7The solution of an equation is also known as its root.
Worked examples
Example 1
Write an equation for the statement: 'The sum of a number and 7 is 15.'
Answer
x + 7 = 15
Always define your variable clearly.
Example 2
Solve the equation: 4y - 3 = 17.
Answer
y = 5
Remember to perform the same operation on both sides to maintain balance.
Example 3
A number when multiplied by 6 and then decreased by 5 gives 19. Find the number.
Answer
The number is 4.
Break down the word problem into smaller parts to form the equation correctly.
Common mistakes
- ✗Forgetting to change the sign of a term when transposing it to the other side of the equation (e.g., changing x + 3 = 7 to x = 7 + 3 instead of x = 7 - 3).
- ✗Performing an operation (like adding or subtracting) on only one side of the equation, thus unbalancing it.
- ✗Confusing an expression with an equation; an expression does not have an equality sign.
- ✗Making errors in basic arithmetic operations, especially with negative numbers.
- ✗Not checking the solution by substituting it back into the original equation to verify its correctness.
Exam tips
- ★Read the problem statement carefully to understand what is given and what needs to be found.
- ★Always define the variable clearly at the beginning of your solution (e.g., 'Let the number be x').
- ★Show all steps of your working clearly and systematically, especially when solving equations, as this helps in earning partial marks.
- ★After finding the solution, always check your answer by substituting the value of the variable back into the original equation.
- ★For word problems, write the final answer in a complete sentence, stating what the variable represents.
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