CBSE Class 7 Mental Maths Simple Equations Worksheet - Free Printable

Problem Analysis:

The image contains a section from "Chapter 4: Simple Equations." It includes key points to remember about linear equations and several questions related to forming, solving, and interpreting simple equations. Below, I will solve the problems step by step.

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Points to Remember:

1. Linear Equation Definition: An equation involving only a linear polynomial (degree 1) is called a linear equation. Examples include:
- \( 7x + 3 = 5 \)
- \( \frac{3}{2}x + 4 = \frac{1}{3} \)

2. Interchange of LHS and RHS: The equation remains the same if the left-hand side (LHS) and right-hand side (RHS) are interchanged.

3. Transposing Terms: Changing terms from one side of the equation to the other is called transposing. When transposing a number, its sign changes. Example:
- \( 12p - 5 = 25 \) becomes \( 12p = 25 + 5 \).

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Questions to Solve:

#### Question 1: Change the given equations into statements.
1. \( 3x + 5 = 27 \)
- Statement: Three times a number plus five equals twenty-seven.

2. \( 7x = 49 \)
- Statement: Seven times a number equals forty-nine.

3. \( 5x + 7 = 9 \)
- Statement: Five times a number plus seven equals nine.

4. \( \frac{x}{3} + 5 = 8 \)
- Statement: One-third of a number plus five equals eight.

5. \( \frac{3}{2}y + 7 = 29 \)
- Statement: Three-halves of a number plus seven equals twenty-nine.

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#### Question 2: Form equations for the following statements.
1. Statement: Five times a number is 25.
- Equation: \( 5x = 25 \)

2. Statement: One-fourth of a number is 20.
- Equation: \( \frac{x}{4} = 20 \)

3. Statement: A number divided by 5 gives seven less than twice the number.
- Let the number be \( x \).
- Twice the number: \( 2x \)
- Seven less than twice the number: \( 2x - 7 \)
- Equation: \( \frac{x}{5} = 2x - 7 \)

4. Statement: Thirteen subtracted from three times a number is 8.
- Let the number be \( x \).
- Three times the number: \( 3x \)
- Thirteen subtracted from three times the number: \( 3x - 13 \)
- Equation: \( 3x - 13 = 8 \)

5. Statement: The length of a rectangle is 8 meters more than its breadth, and its perimeter is 256 meters.
- Let the breadth be \( b \).
- Length: \( b + 8 \)
- Perimeter of a rectangle: \( 2(\text{length} + \text{breadth}) \)
- Equation: \( 2((b + 8) + b) = 256 \)
- Simplify: \( 2(2b + 8) = 256 \)
- Final Equation: \( 4b + 16 = 256 \)

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#### Question 3: Express the given operation in the form of an equation.
- Take any number. Multiply it by 3. Add 49 and divide the result by 7. Then we get 7.
- Let the number be \( x \).
- Multiply by 3: \( 3x \)
- Add 49: \( 3x + 49 \)
- Divide by 7: \( \frac{3x + 49}{7} \)
- Result is 7: \( \frac{3x + 49}{7} = 7 \)
- Equation: \( \frac{3x + 49}{7} = 7 \)

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#### Question 4: Solve the equation and find the value of the variable.
1. \( 3x - 5 = 0 \)
- Add 5 to both sides: \( 3x = 5 \)
- Divide by 3: \( x = \frac{5}{3} \)
- Solution: \( x = \frac{5}{3} \)

2. \( \frac{5}{2}x = 10 \)
- Multiply both sides by \( \frac{2}{5} \): \( x = 10 \cdot \frac{2}{5} \)
- Simplify: \( x = 4 \)
- Solution: \( x = 4 \)

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Final Answers:

1. Statements:
- (i) Three times a number plus five equals twenty-seven.
- (ii) Seven times a number equals forty-nine.
- (iii) Five times a number plus seven equals nine.
- (iv) One-third of a number plus five equals eight.
- (v) Three-halves of a number plus seven equals twenty-nine.

2. Equations:
- (i) \( 5x = 25 \)
- (ii) \( \frac{x}{4} = 20 \)
- (iii) \( \frac{x}{5} = 2x - 7 \)
- (iv) \( 3x - 13 = 8 \)
- (v) \( 4b + 16 = 256 \)

3. Equation: \( \frac{3x + 49}{7} = 7 \)

4. Solutions:
- (i) \( x = \frac{5}{3} \)
- (ii) \( x = 4 \)

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Boxed Final Answer:

\[
\boxed{x = \frac{5}{3}, x = 4}
\]