Solved Questions on Linear Equations in One Variable
1. Solve for x: 2x – 4 = 0
Solution: Add 4 on both sides of the equation
2x – 4 + 4 = 0 + 4
2x = 4
Dividing each side by 2
We get,
2x/2 = 4/2
x = 4/2 = 2
Therefore, x = 2
2. Given the equation: 3x + 4 = 7x - 2
Solution: To solve for the value of x, we first need to get one side of the equation equal to zero. We can do this by subtracting 3x from both sides of the equation: 4 = 4x - 2
Next, we add 2 to both sides of the equation: 6 = 4x
Finally, we divide both sides of the equation by 4 to find the value of x: x = 1.5
So, the solution to the equation is x = 1.5
3. Solve the equation 3x + 6 = 12
Solution: To solve this equation, we need to get x alone on one side of the equation. To do this, we'll subtract 6 from both sides: 3x + 6 = 12
3x = 6
Now we'll divide both sides by 3: 3x/3 = 6/3
x = 2
So, the solution to this equation is x = 2
4. Solve the equation 2x - 4 = 8
Solution: To solve this equation, we need to get x alone on one side of the equation. To do this, we'll add 4 to both sides: 2x - 4 = 8
2x = 12
Now we'll divide both sides by 2: 2x/2 = 12/2
x = 6
So, the solution to this equation is x = 6
5. Solve the equation 4x + 8 = 20 - 2x
Solution: To solve this equation, we'll first simplify the right side: 4x + 8 = 20 - 2x
Now we'll add 2x to both sides: 4x + 8 + 2x = 20
6x + 8 = 20
Now we'll subtract 8 from both sides: 6x + 8 - 8 = 20 - 8
6x = 12
Now we'll divide both sides by 6: 6x/6 = 12/6
x = 2
So, the solution to this equation is x = 2
6. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.
Solution: Let the two numbers be x and y.
It is given that, x + y = 25 and y = x + 9
According to question, x + x + 9 = 25
2x + 9 = 25
2x = 25 - 9 (transposing 9 to the R.H.S changes to -9)
2x = 16
2x/2 = 16/2 (divide by 2 on both sides)
x = 8
Therefore, x + 9 = 8 + 9 = 17
Other number, y = 17
7. Father's age is three more than twice the age of his son. If son's age is 10, what is the father's age?
Solution: Let father's age be "x".
According to the question, 2(10) + 3 = x
x = 23
8. The sum of two consecutive numbers is 53. Find the numbers.
Solution: n + (n + 1) = 2n + 1 = 53
2n = 53 – 1
2n = 52,
n = 52 / 2 = 26
Therefore n = 26
n + 1 = 27
The two numbers are 26 and 27.
9. A rectangle has a length of 12 cm and a perimeter of 40 cm. Write an equation to represent the width, W, of the rectangle.
Solution: The perimeter of a rectangle is the sum of the lengths of all four sides. In this case, we know that the length is 12 cm and the perimeter is 40 cm.
So, we can write: 2(12) + 2W = 40
Simplifying, we get: 24 + 2W = 40
Subtracting 24 from both sides, we get: 2W = 16
Dividing both sides by 2, we get: W = 8
So, the width of the rectangle is 8 cm.
10. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Solution: let's take the youngest child's age is x
so other four children age will become = (x + 3), (x + 6), (x + 9), (x + 12)
Sum of all children age is x + x + 3 + x + 6 + x + 9 + x + 12 = 50
5x + 30 = 50
5x = 50 – 30
5x = 20
x = 4
The age of the youngest child is 4 years.
Practice Questions on Linear Equation in One Variable
1. What is the solution of equation 2x + 3 = 7?
a) x = 2
b) x = -2
c) x = 1
d) x = -1
Answer: a) x = 2
2. If the equation 2x - 3 = 5 is solved for x, what is the value of x?
a) x = 4
b) x = -4
c) x = 2
d) x = -2
Answer: a) x = 4
3. What is the solution of equation 3x + 2 = 6x - 4?
a) x = -3
b) x = -2
c) x = 2
d) x = 3
Answer: c) x = 2
4. If the equation 4x + 5 = 10x - 3 is solved for x, what is the value of x?
a) x = -2
b) x = 2
c) x = 4/3
d) x = -4/3
Answer: c) x = 4/3
5. What is the solution of equation 5x - 6 = 0?
a) x = 0
b) x = 1
c) x = -1
d) x = 6/5
Answer: d) x = 6/5
6. The sum of two consecutive natural numbers is 23. Numbers will be:
a) 11 and 12
b) 11 and 14
c) 11 and 16
d) 11 and 18
Answer: a) 11 and 12
7. The length of a rectangle is twice its breadth. If the perimeter is 72 meters, find the rectangle's length and breadth.
a) Length = 23 cm and breadth = 10 cm
b) Length = 24 cm and breadth = 12 cm
c) Length = 26 cm and breadth = 14 cm
d) Length = 28 cm and breadth = 21 cm
Answer: b) Length = 24 cm and breadth = 12 cm
8. Robert’s father is 4 times as old as Robert. After 5 years, the father will be three times as old as Robert. Find the present age of Robert’s father.
a) 30 years
b) 35 years
c) 40 years
d) 45 years
Answer: c) 40 years
9. If 3/5 of a number is 4 more than 1/2 the number, then what is the number?
a) 40
b) 50
c) 60
d) 70
Answer: a) 40
10. The perimeter of an equilateral triangle is 16.5 cm. Find the length of its side. (in cm)
a) 2 cm
b) 4.5 cm
c) 5.5 cm
d) 5.5 m
Answer: c) 5.5 cm
