## Linear Equations In One Variable

**Class 8**

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*Q & A based on Class 8 NCERT Chapter *

**Q1(MCQ): If 3x – 4 (64 – x) = 10, then the value of x is**

(a) –266

(b) 133

(c) 66.5

(d) 38

Answer: (d)38

3x - 256 + 4x =10

7x = 10 + 256 = 266

x = 266/7 = 38

**Q2: Three consecutive even numbers whose sum is 156 are 51, 52 and 53.**

**State if the above statement is True or False**

Answer: False

Let the three consecutive even numbers be x, x+2, x+4

∴ x + x+ 2 + x+4 = 156

⇒ 3x + 6 = 156

⇒ 3x = 156 - 6 = 150

⇒ x = 150 / 3 = 50

Thus numbers are 50, 51, 52

**Q3: Fifteen added to thrice a whole number gives 93. The number is __________.**

Answer: 26

**Q4: x = –12 is the solution of the linear equation 5x –3(2x + 1) = 21+x (True or False)**

Answer: False

For x = -12,

LHS = 5(-12) -3[2(-12) + 1] = -60 -3[-26+ 1] = -60 -3(25) = -60 + 75 = 15

RHS = 21 + (-12) = 21 - 12 = 9

Thus LHS ≠ RHS

**Q5: The present age of father is four times the age of his son. After 10 years, age of father will become three times the age of his son. Find their present ages.**

Answer: Let the present age of son be x years

∴ The present age of father = 4x years

After 10 years,

Age of son = (x + 10) years

Age of father = (4x + 10) years

According to the given condition

4x + 10 = 3(x + 10)

4x + 10 = 3x + 30

4x – 3x = 30 –10

x = 20

∴ Present age of son = 20 years.

and present age of father = 4x = 4 × 20 = 80 years.

**Q6(MCQ): If 8x – 3 = 25 +17x, then x is**

(a) a fraction

(b) an integer

(c) a rational number

(d) cannot be solved

Answer: (c) a rational number

8x - 3 = 25 + 17x

On transposing,

8x - 17x = 25 + 3

-9x = 28

x = -28/9 which is a rational number.

**Q7(MCQ): The shifting of a number from one side of an equation to other is called**

(a) Transposition

(b) Distributivity

(c) Commutativity

(d) Associativity

Answer: (a) Transposition

**Q8(MCQ): A linear equation in one variable has**

(a) Only one solution

(b) Two solutions

(c) More than two solutions

(d) No solution

Answer: (a) Only one solution

**Q9(MCQ): The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.**

(a) 112

(b) 126

(c) 119

(d) 116

Answer: (a) 112

Let the numbers be x, x+7, x+14

∴ x + x + 7 + x + 14 = 357

⇒ 3x + 21 = 357

⇒ 3x = 357 - 21 = 336

⇒ x 336 / 3 = 112

**Q10: The solution of the equation 3x – 4 = 1 – 2 x is _________.**

Answer: 1

**Q11: In a linear equation, the _________ power of the variable appearing in the equation is one.**

Answer: highest

**Q12: Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.**

Answer: ₹ 4500

Let Kiran gets = ₹p

Salma gets - ₹p + 1000

Jenifer gets = ₹p + 500

∴ Sum is p + p + 1000 + p + 500 = 13500

⇒ 3p = 13500 - 1500 = 12000

⇒ p = 12000/3 = 4000

∴ Jenifer gets = 4000 + 500 = ₹ 4500

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