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All questions of Linear Equations in One Variable for Grade 7 Exam

5 times a number increased by 5 is 25. What is the number 
  • a)
    0
  • b)
    1
  • c)
    7
  • d)
    4
Correct answer is option 'D'. Can you explain this answer?

Let the number be x 
According to question,
5x + 5 = 25 
5x = 20 
x = 4 
So option D is correct. 

Which is a solution of the equation 7x + 5 = 19?
  • a)
    x = 2
  • b)
    x = 3
  • c)
    x = 4
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Madhavan Unni answered
Given equation is 7x + 5 = 19
 7x = 19 - 5
  7x = 14 
Therefore,  x = 2
So option A is the correct answer.  
 

  • a)
    a
  • b)
    b
  • c)
    c
  • d)
    d
Correct answer is option 'D'. Can you explain this answer?

Anoushka Rane answered
Option D is correct answer.
Dividing both sides of the equation by the same number. 

The solution of the equation (a/2)+2=8 is a =
  • a)
    14
  • b)
    16
  • c)
    12
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Shilpa kumar answered
Solution:
Given, (a/2)² = 8
We need to find the value of 'a'.

Step 1: Simplify the given equation
(a/2)² = 8
=> a²/4 = 8
=> a² = 4 × 8
=> a² = 32

Step 2: Find the value of 'a'
Taking square root on both sides, we get
√(a²) = √32
=> a = ± √32

However, we need to choose the positive value of 'a'.
So, a = √32

Step 3: Simplify the value of 'a'
√32 can be written as √16 × √2
=> a = 4 × √2

Therefore, the solution of the equation (a/2)² = 8 is a = 4 × √2, which is approximately equal to 5.66.
Hence, the correct answer is option 'C' (12).

The solution of the equation 3z – 2 = 46 is z =
  • a)
    12
  • b)
    18
  • c)
    16
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Meghana patil answered
The given equation is incomplete. Please provide the complete equation in order to find its solution.

The solution of the equation 5x + 7 = 17 is x =
  • a)
    2
  • b)
    25
  • c)
    5
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Meghana patil answered
**Solution:**

To solve the equation 5x + 7 = 17, we need to find the value of x that makes the equation true.

Let's solve the equation step by step:

Step 1: Subtract 7 from both sides of the equation to isolate the term with x:

5x + 7 - 7 = 17 - 7

This simplifies to:

5x = 10

Step 2: Divide both sides of the equation by 5 to solve for x:

5x/5 = 10/5

This simplifies to:

x = 2

Therefore, the value of x that satisfies the equation is x = 2.

Hence, the correct answer is option 'A' (2).

The solution of the equation 3m/5=6 is m =
  • a)
    12
  • b)
    14
  • c)
    10
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Nisha patel answered
Solution:

To find the solution of the equation 3m/5=6, we need to isolate the variable m on one side of the equal sign.

Step 1: Multiply both sides of the equation by 5 to cancel out the denominator of 3m/5.

3m/5 = 6

5 * 3m/5 = 5 * 6

Step 2: Simplify the left side of the equation by canceling out 5 with 5 in the numerator and denominator.

3m = 30

Step 3: Divide both sides of the equation by 3 to isolate the variable m.

3m/3 = 30/3

m = 10

Therefore, the solution of the equation 3m/5=6 is m = 10, which is option C.

Which is a solution of the equation 2x = 12?
  • a)
    x = 4
  • b)
    x = 6
  • c)
    x = 5
  • d)
    x = 7
Correct answer is option 'B'. Can you explain this answer?

Isolate X.

2x = 12?

Divide by 2 where the x is. What you do to one side you do to the other.

x = 12 divided by 2

12 divided by 2 is 6.

So x = 6

Verify by pluggin in 6 where x is on the original function.

2(6) = 12

Write the statements “One third of a number plus 5 is 8” in the form of equations:
  • a)
    3m + 8 = 5
  • b)
    (1/3)m+8=5
  • c)
    3m + 5 = 8
  • d)
    (1/3)m+5=8
Correct answer is 'D'. Can you explain this answer?

Meera Reddy answered
Take the number to be m. One third of m is m/3.

The number plus 5 is m/3 + 5. It is 8.
The equation then is m/3 + 5 = 8 or (1/3)m + 5 = 8.

Write the statement “p multiplied by 16” in the form of expression.
  • a)
    16p
  • b)
    p + 16
  • c)
    p – 16
  • d)
    16 – p
Correct answer is option 'A'. Can you explain this answer?

Anveshi Shahi answered
If a number is multipled with a variable , we can write it in two ways:
•16×p
or
•16p

According to the options 16p is the correct answer.

The solution of the equation 2m = 7 is m =
  • a)
    14
  • b)
    7/2
  • c)
    2/7
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Explanation:

To solve the equation 2m = 7, we need to isolate the variable m on one side of the equation.

Step 1: Start with the given equation
2m = 7

Step 2: Divide both sides of the equation by 2 to isolate m.
2m/2 = 7/2

Step 3: Simplify both sides of the equation.
m = 7/2

Step 4: The simplified solution of the equation is m = 7/2.

Therefore, the correct answer is option B, 7/2.

Write the statements “One fourth of m is 3 more than 7” in the form of equations:
  • a)
    4m + 7 = 3
  • b)
  • c)
    m/4=3+7
  • d)
    4m + 3 = 7
Correct answer is option 'C'. Can you explain this answer?

1. The sky is blue.
2. I am typing on a keyboard.
3. The sun rises in the east and sets in the west.
4. Water freezes at 0 degrees Celsius.
5. The capital of France is Paris.
6. Dogs are loyal animals.
7. The earth revolves around the sun.
8. Pizza is a popular food.
9. The human body has 206 bones.
10. The Great Wall of China is the longest wall in the world.

Which of the following is an algebraic expression for the statement "The sum of 3x and 11 is 32."?
  • a)
    11x+3=32
  • b)
    3x+11=32  
  • c)
    3x+32=11
  • d)
    11x+32=11
Correct answer is option 'B'. Can you explain this answer?

Shikha rao answered
Unfortunately, the statement is not provided. Therefore, it is not possible to determine which of the following options is the algebraic expression for the statement.

Which of the following is not allowed in any equation?
(a) Adding the same number to both sides of the equation.
(b) Subtracting the same number from both sides of the equation.
(c) Multiplying both sides of the equation by the same non-zero number.
(d) Dividing both sides of the equation by the same number.
  • a)
    a
  • b)
    b
  • c)
    c
  • d)
    d
Correct answer is option 'D'. Can you explain this answer?

Dividing both sides of the equation by the same non-zero number is allowed in a given equation.
► Division of any number by zero is not allowed as set division of number by zero is not defined.
Note: If we put same number to both sides of the equation while adding or subtracting, then there will be no change in the given equation. 

The solution of the equation 20m/3 = 40 is m =
  • a)
    5
  • b)
    6
  • c)
    7
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Khusboo garg answered
To solve the equation 20m/3 = 40, we need to isolate the variable m on one side of the equation.

Step 1: Multiply both sides of the equation by 3 to eliminate the fraction:
(20m/3) * 3 = 40 * 3

This simplifies to:
20m = 120

Step 2: Divide both sides of the equation by 20 to solve for m:
(20m)/20 = 120/20

This simplifies to:
m = 6

Therefore, the solution to the equation 20m/3 = 40 is m = 6.

The solution of the equation p + 4 = 15 is p =
  • a)
    12
  • b)
    15
  • c)
    11
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Sonia Menon answered
To solve the equation p + 4 = 15, we need to isolate the variable p on one side of the equation. Here's a step-by-step explanation:

Step 1: Start with the given equation: p + 4 = 15

Step 2: To isolate the variable p, we need to get rid of the constant term 4. We can do this by subtracting 4 from both sides of the equation:
p + 4 - 4 = 15 - 4
p = 11

Step 3: The final step is to simplify the equation. Since there are no like terms to combine, the equation is already simplified.

Therefore, the solution to the equation p + 4 = 15 is p = 11.

Explanation:
The equation p + 4 = 15 is an algebraic equation with a variable p. The goal is to determine the value of p that satisfies the equation. In order to do this, we perform the same operation on both sides of the equation to keep it balanced.

In this case, we want to isolate the variable p by getting rid of the constant term 4. To do this, we subtract 4 from both sides of the equation. This cancels out the 4 on the left side, leaving us with just p. On the right side, we subtract 4 from 15, which gives us 11.

So the final solution to the equation is p = 11. This means that when we substitute 11 for p in the original equation, the equation is true: 11 + 4 = 15.

The solution of the equation 3x + 7 = 25 is x =
  • a)
    6
  • b)
    4
  • c)
    5
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Sonia kumar answered
To find the solution to the equation 3x - 7 = 25, we need to isolate the variable x.

We can solve this equation by performing inverse operations to eliminate the constant term and isolate the variable.

Here are the steps to solve the equation:

Step 1: Add 7 to both sides of the equation to cancel out the -7 on the left side:
3x - 7 + 7 = 25 + 7
3x = 32

Step 2: Divide both sides of the equation by 3 to isolate the variable x:
3x/3 = 32/3
x = 32/3

Now let's simplify the solution:

Step 3: Divide 32 by 3:
x = 10.6667

Since the given options are whole numbers, we need to round our solution to the nearest whole number.

Rounding 10.6667 to the nearest whole number gives us 11, which is not one of the options given.

Therefore, the correct answer is d) None of these.

It's important to note that the given equation 3x - 7 = 25 does not have a whole number solution. If there were any decimal options in the given choices, we could have chosen the closest one to 10.6667 as the solution. However, in this case, none of the options match the exact solution.

Therefore, the correct answer is d) None of these.

Arjun has 8 candies more than twice the candies Riya has. Arjun has 30 candies. How many candies does Riya have?
  • a)
    10
  • b)
    12
  • c)
    11
  • d)
    15
Correct answer is option 'C'. Can you explain this answer?

Bhaskar Patel answered
Understanding the Problem
Arjun has a certain number of candies, and the relationship between his candies and Riya's candies is given. Let's break down the information:
Given Information:
- Arjun has 30 candies.
- The statement "Arjun has 8 candies more than twice the candies Riya has" can be expressed mathematically.
Setting up the Equation
Let Riya's candies be represented by the variable "R". According to the problem:
- Twice the number of Riya's candies is 2R.
- Arjun has 8 more than that, which can be expressed as:
Arjun's candies = 2R + 8
Since we know that Arjun has 30 candies, we can set up the equation:
- 2R + 8 = 30
Solving the Equation
To find out how many candies Riya has, we will solve the equation step by step:
1. Subtract 8 from both sides:
- 2R + 8 - 8 = 30 - 8
- 2R = 22
2. Now, divide both sides by 2:
- R = 22 / 2
- R = 11
Conclusion
Therefore, Riya has 11 candies. This matches option 'b' in the provided choices.
Final Answer: Riya has 11 candies.

Write the statements “Seven times a number plus 7 gets you 77”in the form of equations:
  • a)
    7x + 7 = 77
  • b)
    7x – 7 = 77
  • c)
    7x + 6 = 66
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

I am a human.
The sky is blue.
Water is essential for life.
I love chocolate.
The Earth revolves around the Sun.
Mathematics is a universal language.
Exercise is good for your health.
The United States is a democratic country.
Reading is a great way to relax.
Animals have different types of habitats.

The solution of the equation x/5=3 is x =
  • a)
    3
  • b)
    15
  • c)
    5
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Sagar Malik answered
Solution:

To solve the equation x/5=3, we need to isolate the variable x on one side of the equation.

Step 1: Multiply both sides of the equation by 5 to eliminate the fraction.

x/5 = 3
5(x/5) = 5(3)
x = 15

Therefore, the solution of the equation x/5=3 is x = 15.

Explanation:

The equation x/5=3 can be read as "x divided by 5 is equal to 3". To solve for x, we need to find the value of x that makes this equation true.

Multiplying both sides of the equation by 5 eliminates the fraction, giving us x = 15. This means that if we substitute 15 for x in the original equation, we get:

15/5 = 3

which is true. Therefore, x = 15 is the solution to the equation x/5 = 3.

Conclusion:

The correct answer to the question is option B, which is 15. By multiplying both sides of the equation x/5=3 by 5, we eliminate the fraction and solve for x, which gives us x = 15.

Chapter doubts & questions for Linear Equations in One Variable - Mathematics for Grade 7 2025 is part of Grade 7 exam preparation. The chapters have been prepared according to the Grade 7 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Grade 7 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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