CBSE Class 7 Maths: Simple Equations - Exercise 4.1 Explained

What are Simple Equations?

A simple equation is a mathematical statement that shows two expressions are equal. It always contains an equality sign (=). For example, x + 5 = 10 is a simple equation. Here, x is a variable, which is a letter that represents an unknown number. The numbers like 5 and 10 are constants because their values don't change. The expressions on either side of the equals sign are called the Left Hand Side (LHS) and the Right Hand Side (RHS).

For an equation to be true, the value of the LHS must be exactly equal to the value of the RHS. Finding the value of the variable that makes the equation true is called solving the equation. In Exercise 4.1, you'll practice identifying these parts and verifying if a given value works as a solution.

Key components of a Simple Equation:

• Variable: A letter (like x, y, a, b) representing an unknown quantity.
• Constant: A fixed numerical value.
• Algebraic Expression: A combination of variables, constants, and mathematical operations (e.g., x + 5, 2y - 3).
• Equality Sign (=): Connects two expressions, stating they have the same value.

Example: In 2y - 3 = 7:

• y is the variable.
• 2, 3, 7 are constants.
• 2y - 3 is the LHS.
• 7 is the RHS.

Step-by-Step: Forming Simple Equations from Word Problems

1. Understand the Unknown — Read the statement carefully and identify the quantity you don't know. Let this unknown quantity be represented by a variable (e.g., x, y, a, p).
2. Identify Mathematical Operations — Look for keywords that indicate mathematical operations: 'sum' or 'more than' means addition (+), 'difference' or 'less than' means subtraction (-), 'product' or 'times' means multiplication (×), 'quotient' or 'divided by' means division (÷).
3. Break Down the Statement into Expressions — Translate parts of the sentence into algebraic expressions. For example, 'seven more than a number' becomes x + 7, and 'four times a number' becomes 4x.
4. Form the Equality — Look for words like 'is', 'equals', 'gives', or 'results in' to identify where the equality sign (=) should be placed. Connect the two expressions you formed with an equals sign.

Worked Examples: Verifying if a Value Satisfies an Equation

• Example 1: Check if x = 3 is a solution for x + 7 = 10. Step 1: Write down the equation: x + 7 = 10. Step 2: Substitute the given value of x into the LHS: LHS = x + 7 = 3 + 7 = 10. Step 3: Compare the LHS with the RHS: LHS = 10, RHS = 10. Since LHS = RHS, the equation is satisfied. Conclusion: Yes, x = 3 is a solution to x + 7 = 10.
• Example 2: Check if m = 5 is a solution for 3m - 2 = 13. Step 1: Write down the equation: 3m - 2 = 13. Step 2: Substitute m = 5 into the LHS: LHS = 3m - 2 = 3(5) - 2 = 15 - 2 = 13. Step 3: Compare the LHS with the RHS: LHS = 13, RHS = 13. Since LHS = RHS, the equation is satisfied. Conclusion: Yes, m = 5 is a solution to 3m - 2 = 13.
• Example 3: Check if y = -2 is a solution for 5y + 1 = 11. Step 1: Write down the equation: 5y + 1 = 11. Step 2: Substitute y = -2 into the LHS: LHS = 5y + 1 = 5(-2) + 1 = -10 + 1 = -9. Step 3: Compare the LHS with the RHS: LHS = -9, RHS = 11. Since LHS ≠ RHS, the equation is not satisfied. Conclusion: No, y = -2 is not a solution to 5y + 1 = 11.

Exam Tip: Avoiding Common Mistakes in Simple Equations

When working with simple equations, especially in Exercise 4.1, students often make a few common errors. Be careful with these:

1. Confusing expressions with equations: Remember, an equation must have an equality sign (=). An expression like x + 5 is not an equation.
2. Incorrect translation of word problems: 'Twice a number' means 2x, not x + 2. 'A number divided by 3' means x/3, not 3/x (unless specified). Pay close attention to the order of operations and keywords.
3. Substitution errors: When substituting a value for the variable, especially negative numbers or fractions, use brackets. For 3m, if m = -4, then 3(-4) = -12, not 3-4 = -1.
4. Not verifying both sides: Always calculate the full LHS after substitution and compare it to the full RHS. Don't just assume it's correct after a partial calculation.
5. Forgetting the variable: Always define what your variable stands for at the beginning of forming an equation (e.g., 'Let the number be x').

Practice Questions with Solutions

• Q: Write the following statement as an equation: "The sum of three times a number and 4 is 19." A: Step 1: Let the unknown number be 'x'. Step 2: "Three times a number" means 3 * x = 3x. Step 3: "The sum of three times a number and 4" means 3x + 4. Step 4: "is 19" means equals 19. Final answer: 3x + 4 = 19
• Q: Check if p = 6 is a solution to the equation p/2 + 3 = 6. A: Step 1: Write down the equation: p/2 + 3 = 6. Step 2: Substitute p = 6 into the LHS: LHS = 6/2 + 3. Step 3: Calculate the LHS: LHS = 3 + 3 = 6. Step 4: Compare LHS and RHS: LHS = 6, RHS = 6. Since LHS = RHS, the equation is satisfied. Final answer: Yes, p = 6 is a solution.
• Q: Write an equation for the statement: "7 subtracted from one-third of a number is 2." A: Step 1: Let the number be 'y'. Step 2: "One-third of a number" means y/3. Step 3: "7 subtracted from one-third of a number" means y/3 - 7. Step 4: "is 2" means equals 2. Final answer: y/3 - 7 = 2
• Q: Check if n = -1 is a solution to the equation 5n - 7 = 2. A: Step 1: Write down the equation: 5n - 7 = 2. Step 2: Substitute n = -1 into the LHS: LHS = 5(-1) - 7. Step 3: Calculate the LHS: LHS = -5 - 7 = -12. Step 4: Compare LHS and RHS: LHS = -12, RHS = 2. Since LHS ≠ RHS, the equation is not satisfied. Final answer: No, n = -1 is not a solution.

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