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Practice Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions based on the NCERT syllabus. Solve fresh and exam-oriented MCQs on equation solving, variables, inverse operations, verification, and application-based problems.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Simple Equations
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 3
Difficulty Level: Moderate
Based On: NCERT Syllabus
Introduction
A simple equation represents a mathematical relationship involving an unknown quantity. The unknown is generally represented by a variable such as $$x$$.
For example:
$$3x+5=20$$
To find the value of $$x$$, we use inverse operations and maintain equality on both sides.
In Practice Set 3, students will work with equations involving multiplication, division, addition, subtraction, and simple application-based situations.
What You Will Learn
✔ Solving equations involving more than one operation
✔ Using inverse operations correctly
✔ Finding unknown values
✔ Verifying solutions
✔ Translating statements into equations
✔ Solving simple word problems
Why This Topic Is Important
Simple equations help students develop algebraic thinking. They provide a systematic way to find unknown quantities and are useful in many mathematical and real-life situations.
A strong understanding of equations also prepares students for more advanced algebra in higher classes.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ State Board Exams
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ NCERT-Based Practice
✔ Mathematics Revision
Q1. Find the value of $$x$$:
$$3x+4=19$$
A) $$4$$
B) $$5$$
C) $$6$$
D) $$7$$
Answer:
B) $$5$$
Useful Concept
When an equation contains multiplication and addition, first remove the constant term and then divide by the coefficient of the variable.
Solution
Given:
$$3x+4=19$$
Subtract $$4$$ from both sides:
$$3x+4-4=19-4$$
$$3x=15$$
Now divide both sides by $$3$$:
$$x=\frac{15}{3}$$
Therefore:
$$x=5$$
Verification
Substitute $$x=5$$:
$$3(5)+4=15+4=19$$
Thus:
$$19=19$$
The solution is correct.
Hence, the correct answer is:
B) $$5$$
Q2. If
$$4x-7=21,$$
then the value of $$x$$ is:
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Answer:
C) $$7$$
Useful Concept
First remove the number being subtracted, then divide by the coefficient of the variable.
Solution
Given:
$$4x-7=21$$
Add $7$ to both sides:
$$4x-7+7=21+7$$
$$4x=28$$
Divide both sides by $$4$$:
$$x=\frac{28}{4}$$
Therefore:
$$x=7$$
Verification
$$4(7)-7=28-7=21$$
Therefore, the solution is correct.
Hence, the correct answer is:
C) $$7$$
Q3. Which equation represents the statement:
“Five times a number decreased by 3 is 22”?
A) $$5x+3=22$$
B) $$5x-3=22$$
C) $$5(x-3)=22$$
D) $$x-5+3=22$$
Answer:
B) $$5x-3=22$$
Useful Concept
The phrase “five times a number” means $$5x$$, while “decreased by 3” means subtracting $$3$$.
Solution
Let the number be:
$$x$$
Five times the number:
$$5x$$
Five times the number decreased by $$3$$:
$$5x-3$$
According to the question, this equals $$22$$:
$$5x-3=22$$
Therefore, the required equation is:
B) $$5x-3=22$$
We can also solve it:
$$5x-3=22$$
Add $$3$$:
$$5x=25$$
Divide by $$5$$:
$$x=5$$
Verification:
$$5(5)-3=25-3=22$$
So the equation is correct.
Q4. The perimeter of a square is $$$36$ cm. If the side length is $$x$$ cm, which equation can be used to find $$x$$?
A) $$x+4=36$$
B) $$2x=36$$
C) $$4x=36$$
D) $$x-4=36$$
Answer:
C) $$4x=36$$
Useful Concept
A square has four equal sides.
Therefore:
$$\text{Perimeter}=4\times\text{side}$$
Solution
Let the side of the square be:
$$x\text{ cm}$$
The perimeter of a square is:
$$4x$$
Given perimeter:
$$36\text{ cm}$$
Therefore:
$$4x=36$$
Hence, the correct equation is:
C) $$4x=36$$
Solving:
$$x=\frac{36}{4}$$
$$x=9$$
Thus, the side length is $$9$$ cm.
Verification:
$$4(9)=36$$
Therefore, the equation is correct.
Q5. A number is multiplied by $$6$$ and then $$5$$ is added to the result. The final result is $$35$$. What is the number?
A) $$4$$
B) $$5$$
C) $$6$$
D) $$7$$
Answer:
B) $$5$$
Useful Concept
Translate the operations in the same order as given in the question.
Solution
Let the number be:
$$x$$
The number is multiplied by $$6$$:
$$6x$$
Then $5$ is added:
$$6x+5$$
The final result is $$35$$:
$$6x+5=35$$
Subtract $$5$$ from both sides:
$$6x=30$$
Divide by $$64$:
$$x=5$$
Verification
$$6(5)+5=30+5=35$$
Therefore, the number is:
$$5$$
Hence, the correct answer is:
B) $$5$$
Important Formulas & Concepts
Equation with Addition
$$ax+b=c$$
First subtract $$b$$:
$$ax=c-b$$
Then divide by $$a$$:
$$x=\frac{c-b}{a}$$
Equation with Subtraction
$$ax-b=c$$
Add $$b$$ to both sides:
$$ax=c+b$$
Therefore:
$$x=\frac{c+b}{a}$$
Perimeter of a Square
If side length is $$x$$:
$$P=4x$$
Translating Common Words
Sum → Addition
$$x+a$$
Difference → Subtraction
$$x-a$$
Product → Multiplication
$$ax$$
Quotient → Division
$$\frac{x}{a}$$
Increased by → Addition
Decreased by → Subtraction
Verification
After obtaining the value of the variable, substitute it into the original equation.
If both sides are equal, the answer is verified.
Related Practice Questions
Q1. Solve:
$$2x+7=19$$
Q2. Find $$x$$:
$$5x-4=31$$
Q3. Write an equation for:
Four times a number increased by 2 is 30.
Q4. The perimeter of a square is $$484$ cm. Find its side.
Q5. A number is multiplied by $$3$$ and $$44$$ is added to it to get $$25$$. Find the number.
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find $$x$$:
$$2x+5=17$$
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Q2. Find $x$:
$$3x-4=20$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$94$
Q3. Which equation represents “four times a number plus 7 is 31”?
A) $44x-7=31$$
B) $$4x+7=31$$
C) $$x+4+7=31$$
D) $47x+4=31$$
Q4. A square has perimeter $$28$$ cm. Its side is:
A) $$5$$ cm
B) $$6$$ cm
C) $$7$$ cm
D) $$8$$ cm
Q5. If:
$$5x+2=27,$$
then $$x$$ is:
A) $$4$$
B) $$5$$
C) $$6$$
D) $$7$$
Exam Tips
✔ Solve equations step by step.
✔ Remove addition or subtraction before dividing by the coefficient.
✔ Carefully translate words into mathematical operations.
✔ Remember that a square has four equal sides.
✔ Check whether your final value satisfies the original equation.
✔ Write units such as cm when solving measurement problems.
✔ Avoid skipping intermediate calculations in examination answers.
Quick Revision Notes
✔ An equation expresses equality.
✔ A variable represents an unknown quantity.
✔ For:
$$ax+b=c$$
subtract $b$ first and then divide by $$a$$.
✔ For:
$$ax-b=c$$
add $$b$$ first and then divide by $$a$$.
✔ Square perimeter:
$$P=4x$$
✔ “Times” generally indicates multiplication.
✔ “Increased by” indicates addition.
✔ “Decreased by” indicates subtraction.
✔ Always verify the solution.
Common Mistakes Students Make
❌ Writing $$5x+3$$ instead of $$5x-3$$ for “decreased by 3”.
❌ Dividing before removing the constant term without proper algebraic steps.
❌ Forgetting that a square has four equal sides.
❌ Confusing multiplication with addition.
❌ Ignoring the order of operations described in a word problem.
❌ Not checking whether the final value satisfies the original equation.
Key Takeaways
✔ Simple equations can contain multiple operations.
✔ Inverse operations help isolate the variable.
✔ Word problems can be converted into equations.
✔ Mathematical statements should be translated carefully.
✔ Perimeter formulas can be used to form equations.
✔ Verification is an important part of solving equations.
FAQs
Q. How do we solve an equation such as $$3x+4=19$$?
Answer:
First subtract $$4$$ from both sides:
$$3x=15$$
Then divide by $$3$$:
$$x=5$$
Q. What does “decreased by” mean?
Answer:
“Decreased by” means subtraction.
For example, “a number decreased by $$4$$” is represented by:
$$x-4$$
Q. What does “five times a number” mean?
Answer:
If the number is $$x$$, then five times the number is:
$$5x$$
Q. What is the perimeter of a square?
Answer:
If the side of a square is $$x$$, then its perimeter is:
$$4x$$
Q. Why is verification important?
Answer:
Verification confirms that the value found for the variable actually satisfies the original equation.
Conclusion
These Class 7 Maths Chapter 4 Simple Equations MCQ Questions with Answers and Solutions – provide fresh practice on equations involving multiple operations, mathematical statements, perimeter-based equations, and application-based problems.
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