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Practice each question, then open the answer or worked solution.
The solution of the equation ax + b = 0 is
(a) a/b (b) –b (c) –b/a (d) b/a
Solution:-
(c) –b/a
Consider the given equation ax + b = 0
Transpose ‘b’ to right hand side then it becomes –b.
ax = -b
x = -b/a
If a and b are positive integers, then the solution of the equation ax = b will always be a
(a) positive number (b) negative number (c) 1 (d) 0
Solution:-
(a) positive number
The solution of the given equation ax = b
x = b/a
Which of the following is not allowed in a given equation?
Solution:-
(d) Dividing both sides of the equation by the same number.
The solution of which of the following equations is neither a fraction nor an integer? (a) 2x + 6 = 0 (b) 3x – 5 = 0
(c) 5x – 8 = x + 4 (d) 4x + 7 = x + 2
Solution:-
(d) 4x + 7 = x + 2
Consider the equation 4x + 7 = x + 2
Transpose 7 to right hand side then it becomes –7 and x to Left hand side then it becomes – x.
4x – x = 2 – 7
3x = -5
x = -5/3
The equation which cannot be solved in integers is
(a) 5y – 3 = – 18 (b) 3x – 9 = 0
(c) 3z + 8 = 3 + z (d) 9y + 8 = 4y – 7
Solution:-
(c) 3z + 8 = 3 + z
Consider the equation 3z + 8 = 3 + z
Transpose 8 to right hand side then it becomes –8 and z to Left hand side then it becomes – z.
3z – z = 3 – 8
2z = -5
z = -5/2
If 7x + 4 = 25, then x is equal to
(a) 29/7 (b) 100/7 (c) 2 (d) 3
Solution:-
(d) 3
Consider the given equation 7x + 4 = 25
Transpose 4 to right hand side then it becomes –4
7x = 25 – 4
7x = 21
x = 21/7
x = 3
The solution of the equation 3x + 7 = – 20 is
(a) 17/7 (b) -9 (c) 9 (d) 13/3
Solution:-
(b) -9
Consider the given equation 3x + 7 = – 20
Transpose 7 to right hand side then it becomes –7
3x = -20 – 7
3x = -27
x = -27/3
x = -9
The value of y for which the expressions (y – 15) and (2y + 1) become equal is
(a) 0 (b) 16 (c) 8 (d) – 16
Solution:-
(d) – 16
Consider the given equation (y – 15) = (2y + 1)
Transpose -15 to right hand side then it becomes 15 and 2y to Left hand side then it becomes – 2y.
y – 2y = 15 + 1
-y = 16
y = -16
If k + 7 = 16, then the value of 8k – 72 is
(a) 0 (b) 1 (c) 112 (d) 56
Solution:-
(a) 0
Consider the given equation k + 7 = 16
To find out the value of K.
Transpose 7 to right hand side then it becomes -7
k = 16 – 7
k = 9
Then, the value of 8k – 72 will be,
= (8 × 9) – 72
= 72 – 72
= 0
If 43m = 0.086, then the value of m is
(a) 0.002 (b) 0.02 (c) 0.2 (d) 2
Solution:-
(a) 0.002
Consider the given equation 43m = 0.086
To find out the value of m.
m = 0.086/43
m = 0.002