Chapter 4: Linear Equations in one Variable

1: If x = a, then which of the following is not always true for an integer k.
(a) kx = ak               (b) xk=ak
(c) x – k = a – k     (d) x + k = a + k
Ans: (b).

2: If 3x – 4 (64 – x) = 10, then the value of x is
(a) – 266              (b) 133          (c) 66.5              (d) 38
Ans: (d).

1.The solution of which of the following equations is neither a fraction nor an integer.
(a)3x + 2 = 5x + 2(b)4x – 18 = 2
(c)4x + 7 = x + 2(d)5x – 8 = x + 4
2.The solution of the equation ax + b = 0 is
(a)axb=(b)x = –b
(c)bxa
−=(d)bxa

3.If 8x – 3 = 25 +17x, then x is
(a)a fraction(b)an integer
(c)a rational number(d)cannot be solved
4.The shifting of a number from one side of an equation to other is
called
(a)Transposition(b)Distributivity
(c)Commutativity(d)Associativity
5.If 543
x− = 2
5
x, then the numerical value of 2x – 7 is
(a)19
13(b)13
19−(c)0(d)13
19
6.The value of x for which the expressions 3x – 4 and 2x + 1 become
equal is
(a)–3(b)0(c)5(d)1
7.If a and b are positive integers, then the solution of the equation
ax = b has to be always
(a)positive(b)negative(c)one(d)zero

8.Linear equation in one variable has
(a)only one variable with any power.
(b)only one term with a variable.
(c)only one variable with power 1.
(d)only constant term.

9.Which of the following is a linear expression:
(a)x2 + 1(b)y + y2(c)4(d)1 + z
10.A linear equation in one variable has
(a)Only one solution
(b)Two solutions
(c)More than two solutions
(d)No solution
11.Value of S in 1
3 + S = 2
5
(a)4
5(b)1
15(c)10(d)0
12.4
3
−y = 3
4−, then y =
(a)
2
3
4

−    (b)
2
4
3

−    (c)
2
3
4

    (d)
2
4
3

   

13.The digit in the tens place of a two digit number is 3 more than the
digit in the units place. Let the digit at units place be b. Then the
number is
(a)11b + 30(b)10b + 30(c)11b + 3(d)10b + 3
14.Arpita’s present age is thrice of Shilpa. If Shilpa’s age three years ago
was x. Then Arpita’s present age is
(a)3(x – 3)(b)3x + 3
(c)3x – 9(d)3(x + 3)

15.The sum of three consecutive multiples of 7 is 357. Find the smallest
multiple.
(a)112(b)126
(c)119(d)116

16.In a linear equation, the _________ power of the variable appearing in
the equation is one.
17.The solution of the equation 3x – 4 = 1 – 2 x is _________.
18.The solution of the equation 2y = 5y – 18
5 is _________.
19.Any value of the variable which makes both sides of an equation

equal is known as a _________ of the equation.
20.9x – _________ = –21 has the solution (–2)
21.Three consecutive numbers whose sum is 12 are _________, _________

and _________.
22.The share of A when Rs 25 are divided between A and B so that A

gets Rs. 8 more than B is _________.
23.A term of an equation can be transposed to the other side by changing

its _________.
24.On subtracting 8 from x, the result is 2. The value of x is _________.
25.305
x+ = 18 has the solution as _________.

26.When a number is divided by 8, the result is –3. The number is

_________.
27.9 is subtracted from the product of p and 4, the result is 11. The
value of p is _________.
28.If 225x− = 355x−, then x = _________.
29.After 18 years, Swarnim will be 4 times as old as he is now. His

present age is _________.
30.Convert the statement Adding 15 to 4 times x is 39 into an equation
_________.