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All questions of Linear Equations in one Variable for Class 8 Exam
What is the first step to solve the equation 2x + 5 = 11?- a)Add 5 to both sides
- b)Subtract 5 from both sides
- c)Multiply both sides by 2
- d)Divide both sides by 2
Correct answer is option 'B'. Can you explain this answer?
What is the first step to solve the equation 2x + 5 = 11?
a)
Add 5 to both sides
b)
Subtract 5 from both sides
c)
Multiply both sides by 2
d)
Divide both sides by 2
 | EduRev Class 8 answered |
To isolate the variable in the equation 2x + 5 = 11, the first step is to subtract 5 from both sides, resulting in 2x = 6. This allows us to further solve for x.
How do you represent consecutive multiples of 3 starting with x?- a)x, x + 1, x + 2
- b)x, x + 3, x + 6
- c)x, x + 2, x + 4
- d)x, x + 3, x + 9
Correct answer is option 'B'. Can you explain this answer?
How do you represent consecutive multiples of 3 starting with x?
a)
x, x + 1, x + 2
b)
x, x + 3, x + 6
c)
x, x + 2, x + 4
d)
x, x + 3, x + 9
 | Sakshi Chauhan answered |
Understanding Consecutive Multiples
To represent consecutive multiples of 3 starting with a number x, we must remember what a multiple of 3 is. A multiple of a number is obtained by multiplying that number by an integer.
Definition of Multiples of 3
- The first multiple of 3 after x can be represented as:
- x + (3 - (x mod 3)) if x is not already a multiple of 3.
- If x is a multiple of 3, then the first multiple is simply x.
Consecutive Multiples of 3
- Once we have the starting point, the next consecutive multiples of 3 can be calculated by simply adding 3 repeatedly.
Option Analysis
Let's analyze option B: x, x + 3, x + 6.
- First term:
- The initial term is x.
- Second term:
- The second term is x + 3, which is the next multiple of 3 after x.
- Third term:
- The third term is x + 6, which is 3 added to the previous term (x + 3), making it 2 multiples of 3 after x.
Why Other Options are Incorrect
- Option A: x, x + 1, x + 2
- These are not multiples of 3.
- Option C: x, x + 2, x + 4
- These numbers skip multiples of 3.
- Option D: x, x + 3, x + 9
- This skips the multiple x + 6, making it incorrect.
Conclusion
Thus, the correct representation of consecutive multiples of 3 starting with x is option B: x, x + 3, x + 6.
To represent consecutive multiples of 3 starting with a number x, we must remember what a multiple of 3 is. A multiple of a number is obtained by multiplying that number by an integer.
Definition of Multiples of 3
- The first multiple of 3 after x can be represented as:
- x + (3 - (x mod 3)) if x is not already a multiple of 3.
- If x is a multiple of 3, then the first multiple is simply x.
Consecutive Multiples of 3
- Once we have the starting point, the next consecutive multiples of 3 can be calculated by simply adding 3 repeatedly.
Option Analysis
Let's analyze option B: x, x + 3, x + 6.
- First term:
- The initial term is x.
- Second term:
- The second term is x + 3, which is the next multiple of 3 after x.
- Third term:
- The third term is x + 6, which is 3 added to the previous term (x + 3), making it 2 multiples of 3 after x.
Why Other Options are Incorrect
- Option A: x, x + 1, x + 2
- These are not multiples of 3.
- Option C: x, x + 2, x + 4
- These numbers skip multiples of 3.
- Option D: x, x + 3, x + 9
- This skips the multiple x + 6, making it incorrect.
Conclusion
Thus, the correct representation of consecutive multiples of 3 starting with x is option B: x, x + 3, x + 6.
What is the solution to the equation 3y = 9?- a)y = 3
- b)y = 5
- c)y = 6
- d)y = 2
Correct answer is option 'A'. Can you explain this answer?
What is the solution to the equation 3y = 9?
a)
y = 3
b)
y = 5
c)
y = 6
d)
y = 2
| | EduRev Class 8 answered |
To solve 3y = 9, divide both sides by 3, resulting in y = 3. This is a straightforward solution that showcases the basic principle of isolating the variable.
What is the equation formed if x represents the first of two consecutive odd numbers and the sum is 36?- a)x + (x + 4) = 36
- b)x + (x + 1) = 36
- c)x + (x + 2) = 36
- d)x + (x + 3) = 36
Correct answer is option 'C'. Can you explain this answer?
What is the equation formed if x represents the first of two consecutive odd numbers and the sum is 36?
a)
x + (x + 4) = 36
b)
x + (x + 1) = 36
c)
x + (x + 2) = 36
d)
x + (x + 3) = 36
 | Trisha Vashisht answered |
The equation x + (x + 2) = 36 is formed to represent the sum of two consecutive odd numbers. This equation reflects the relationship between the first and the second odd number.
If the perimeter of a rectangle is 26 cm, what is its new perimeter when each side is increased by x cm?- a)26 + 4x
- b)52 + 4x
- c)52 cm
- d)26 + 2x
Correct answer is option 'A'. Can you explain this answer?
If the perimeter of a rectangle is 26 cm, what is its new perimeter when each side is increased by x cm?
a)
26 + 4x
b)
52 + 4x
c)
52 cm
d)
26 + 2x
| | Trisha Vashisht answered |
The new perimeter after increasing each side by x cm would be calculated as 2[(8 + x) + (5 + x)], which simplifies to 26 + 4x. This reflects the increase in perimeter due to the adjustment in dimensions.
Which operation does NOT change the value of the equation?- a)Multiplying both sides by the same non-zero number
- b)Dividing both sides by the same non-zero number
- c)Adding the same number to both sides
- d)Subtracting a different number from both sides
Correct answer is option 'D'. Can you explain this answer?
Which operation does NOT change the value of the equation?
a)
Multiplying both sides by the same non-zero number
b)
Dividing both sides by the same non-zero number
c)
Adding the same number to both sides
d)
Subtracting a different number from both sides
| | EduRev Class 8 answered |
Subtracting a different number from both sides does not maintain the equality of the equation. In contrast, adding, multiplying, or dividing by the same non-zero number keeps the equation balanced.
What would the equation be for the situation where a man is 24 years older than his son?- a)x + 24 = y
- b)y - x = 24
- c)y + 24 = x
- d)x - y = 24
Correct answer is option 'A'. Can you explain this answer?
What would the equation be for the situation where a man is 24 years older than his son?
a)
x + 24 = y
b)
y - x = 24
c)
y + 24 = x
d)
x - y = 24
| | EduRev Class 8 answered |
If we let x represent the age of the son and y represent the age of the man, the equation y = x + 24 correctly expresses that the man is 24 years older than his son. This relationship is crucial for solving age-related problems.
Which of the following statements about linear equations is true?- a)A linear equation can have more than one solution.
- b)A linear equation in one variable has exactly one solution.
- c)A linear equation has an unlimited number of solutions.
- d)A linear equation cannot be graphed.
Correct answer is option 'B'. Can you explain this answer?
Which of the following statements about linear equations is true?
a)
A linear equation can have more than one solution.
b)
A linear equation in one variable has exactly one solution.
c)
A linear equation has an unlimited number of solutions.
d)
A linear equation cannot be graphed.
| | EduRev Class 8 answered |
A linear equation in one variable has exactly one solution, known as its root. This characteristic is fundamental to understanding linear equations and their graphical representation as straight lines.
In the equation 5z - 10 = 0, what is the root of the equation?- a)z = 1
- b)z = 10
- c)z = 0
- d)z = 2
Correct answer is option 'D'. Can you explain this answer?
In the equation 5z - 10 = 0, what is the root of the equation?
a)
z = 1
b)
z = 10
c)
z = 0
d)
z = 2
| | EduRev Class 8 answered |
By adding 10 to both sides of the equation 5z - 10 = 0, we find that 5z = 10. Dividing both sides by 5 gives z = 2, which is the root of the equation.
Which of the following represents consecutive even numbers starting from x?- a)x + 1, x + 3, x + 5
- b)x, x + 2, x + 4
- c)x, x + 1, x + 2
- d)x, x + 1, x + 3
Correct answer is option 'B'. Can you explain this answer?
Which of the following represents consecutive even numbers starting from x?
a)
x + 1, x + 3, x + 5
b)
x, x + 2, x + 4
c)
x, x + 1, x + 2
d)
x, x + 1, x + 3
| | EduRev Class 8 answered |
Consecutive even numbers can be represented as x, x + 2, x + 4, where x is an even integer. This shows the difference of 2 between each successive even number.
What is the next step after solving the equation 3y - 7 = 16 by adding 7 to both sides?- a)Divide both sides by 3
- b)Subtract 3 from both sides
- c)Multiply both sides by 3
- d)Add 3 to both sides
Correct answer is option 'A'. Can you explain this answer?
What is the next step after solving the equation 3y - 7 = 16 by adding 7 to both sides?
a)
Divide both sides by 3
b)
Subtract 3 from both sides
c)
Multiply both sides by 3
d)
Add 3 to both sides
| | EduRev Class 8 answered |
After adding 7 to both sides of the equation 3y - 7 = 16, the next step is to divide both sides by 3 to isolate y. This leads to y = 3 as the solution.
If a linear equation has a root of 4, what does this indicate about the equation?- a)It has no solutions.
- b)It has multiple solutions.
- c)The equation is satisfied when x = 4.
- d)The equation is invalid.
Correct answer is option 'C'. Can you explain this answer?
If a linear equation has a root of 4, what does this indicate about the equation?
a)
It has no solutions.
b)
It has multiple solutions.
c)
The equation is satisfied when x = 4.
d)
The equation is invalid.
| | Trisha Vashisht answered |
A root of 4 means that when x is substituted with 4 in the equation, both sides of the equation are equal. This indicates that x = 4 satisfies the equation, confirming it as a valid solution.
What is the new length of a rectangle if its original length is 8 cm and each side is increased by 6.5 cm?- a)10 cm
- b)8 cm
- c)14.5 cm
- d)20 cm
Correct answer is option 'C'. Can you explain this answer?
What is the new length of a rectangle if its original length is 8 cm and each side is increased by 6.5 cm?
a)
10 cm
b)
8 cm
c)
14.5 cm
d)
20 cm
| | EduRev Class 8 answered |
When the original length of 8 cm is increased by 6.5 cm, the new length becomes 8 + 6.5 = 14.5 cm. This calculation reflects the adjustment made to the rectangle's dimensions.
What is the general form of a linear equation in one variable?- a)ax + b = 0
- b)ax^2 + b = 0
- c)ax^2 + bx + c = 0
- d)ax + b = c
Correct answer is option 'A'. Can you explain this answer?
What is the general form of a linear equation in one variable?
a)
ax + b = 0
b)
ax^2 + b = 0
c)
ax^2 + bx + c = 0
d)
ax + b = c
| | Trisha Vashisht answered |
A linear equation in one variable is expressed in the form ax + b = 0, where 'a' and 'b' are constants, and 'a' cannot equal zero. This form signifies that the equation represents a straight line when graphed.
What is the first step in solving the word problem: "A number is such that twice the number is 10 more than the number itself"?- a)Form the equation 2x = x - 10
- b)Form the equation 2x = x + 10
- c)Let the number be x
- d)Let the number be y
Correct answer is option 'B'. Can you explain this answer?
What is the first step in solving the word problem: "A number is such that twice the number is 10 more than the number itself"?
a)
Form the equation 2x = x - 10
b)
Form the equation 2x = x + 10
c)
Let the number be x
d)
Let the number be y
| | EduRev Class 8 answered |
In this problem, we start by representing the unknown number as x. This allows us to form the equation based on the relationship described, which is 2x = x + 10.
When solving the equation 2x - 3 = 7, what is the correct operation to isolate x?- a)Subtract 3 from both sides
- b)Divide both sides by 2
- c)Multiply both sides by 2
- d)Add 3 to both sides
Correct answer is option 'D'. Can you explain this answer?
When solving the equation 2x - 3 = 7, what is the correct operation to isolate x?
a)
Subtract 3 from both sides
b)
Divide both sides by 2
c)
Multiply both sides by 2
d)
Add 3 to both sides
| | EduRev Class 8 answered |
To isolate x in the equation 2x - 3 = 7, the correct first step is to add 3 to both sides, resulting in 2x = 10. This prepares for the next step of dividing by 2 to find x.
What is the solution to the equation 2x - 1 = 3?- a)x = 3
- b)x = 4
- c)x = 1
- d)x = 2
Correct answer is option 'D'. Can you explain this answer?
What is the solution to the equation 2x - 1 = 3?
a)
x = 3
b)
x = 4
c)
x = 1
d)
x = 2
| | Trisha Vashisht answered |
To solve the equation 2x - 1 = 3, first add 1 to both sides, yielding 2x = 4. Then, dividing by 2 gives x = 2. This solution illustrates the step-by-step process of isolating the variable.
In the equation 2x = 10, what is the next step after dividing both sides by 2?- a)x = 10
- b)x = 20
- c)x = 2
- d)x = 5
Correct answer is option 'D'. Can you explain this answer?
In the equation 2x = 10, what is the next step after dividing both sides by 2?
a)
x = 10
b)
x = 20
c)
x = 2
d)
x = 5
| | Trisha Vashisht answered |
After dividing both sides of 2x = 10 by 2, we obtain x = 5. This is the solution that satisfies the equation, demonstrating the isolation of the variable.
What is the solution to the equation 4x - 8 = 0?- a)x = 4
- b)x = 0
- c)x = 2
- d)x = -2
Correct answer is option 'C'. Can you explain this answer?
What is the solution to the equation 4x - 8 = 0?
a)
x = 4
b)
x = 0
c)
x = 2
d)
x = -2
| | Trisha Vashisht answered |
To solve 4x - 8 = 0, first add 8 to both sides to get 4x = 8, and then divide by 4, resulting in x = 2. This is the value that satisfies the equation.
What is the process to solve a word problem involving linear equations?- a)Solve the problem without forming an equation
- b)Ignore the details of the problem
- c)Identify the known and unknown quantities, then form an equation
- d)Guess the answer
Correct answer is option 'C'. Can you explain this answer?
What is the process to solve a word problem involving linear equations?
a)
Solve the problem without forming an equation
b)
Ignore the details of the problem
c)
Identify the known and unknown quantities, then form an equation
d)
Guess the answer
| | Trisha Vashisht answered |
The correct approach to solving word problems is to carefully identify the known and unknown quantities and then form an appropriate equation based on the relationships described. This structured method ensures a logical solution.
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