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Practice each question, then open the answer or worked solution.
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
Solution:-
(c) 4x + 7 = x + 2
Transposing 7 to RHS and it becomes -7 and x to LHS, it becomes -x
4x – x = 2 – 7
3x = – 5
X = -5/3
So, -5/3 is neither a fraction nor an integer.
The solution of the equation ax + b = 0 is
(a) x = a/b (b) x = -b
(c) x = -b/a (d) x = b/a
Solution:-
(c) x = -b/a
Given, ax + b = 0
Transposing b to RHS and it becomes -b
Then,
ax = -b
x = -b/a
If 8x – 3 = 25 +17x, then x is
(a) a fraction (b) an integer
(c) a rational number (d) cannot be solved
Solution:-
(c) a rational number
Given, 8x – 3 = 25 + 17x
Transposing -3 to RHS and it becomes 3, and 17x to LHS, it becomes -17x.
8x – 17x = 25 + 3
-9x = 28
X = -28/9
Therefore x is a rational number.
The shifting of a number from one side of an equation to the other is called
(a) Transposition (b) Distributivity
(c) Commutativity (d) Associativity
Solution:-
(a) Transposition
The shifting of a number from one side of an equation to other is called Transposition
If (5x/3) – 4 = (2x/5), then the numerical value of 2x – 7 is
(a) 19/13 (b) -13/19 (c) 0 (d) 13/19
Solution:-
(b) -13/19
Given, (5x/3) – 4 = (2x/5)
(5x/3) – (2x/5) = 4
LCM of 3 and 5 is 15
(25x – 6x)/15 = 4
19x = 4 × 15
19x = 60
X = 60/19
Then, Substitute the value of x in 2x -7
= (2 × (60/19)) – 7
= (120/19) – 7
= (120 – 133)/19
= – 13/19
The value of x for which the expressions 3x – 4 and 2x + 1 become equal is
(a) -3 (b) 0 (c) 5 (d) 13/19
Solution:-
(c) 5
Given, 3x – 4 = 2x + 1
Transposing -4 to RHS and it becomes 4, and 2x to LHS, it becomes -2x.
3x – 2x = 1 + 4
X = 5
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
Solution:-
(a) positive
Let a = 3, b = 4
Then, ax = b
3x = 4
X = 4/3
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.
Solution:-
(c) only one variable with power 1.
Which of the following is a linear expression:
(a) x2 + 1 (b) y + y2 (c) 4 (d) 1 + z
Solution:-
(d) 1 + z
The linear expression is one which has the highest power as 1.
A linear equation in one variable has
(a) Only one solution
(b) Two solutions
(c) More than two solutions
(d) No solution
Solution:-
(a) Only one solution