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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

x 9 6
1
3. Assertion (A): The solution of the equation += is .
3 15 5
reason (r): To solve the linear equation with fractions, multiply both side of equation by the LCM
of denominators.
4. Assertion (A): If seven times a number is equal to 56 minus three times the same number. The
number is 14.
reason (r): To solve a linear equation with variable on both sides, we use transposition method.

C. Fill in the blanks.
1. If 3a + 14 = 9 + 5a, then value of a is ............... .
2. On subtracting 6 from a, the result is 3. The value of a is ............... .

3. If 2 times a number is 20, then the number is ............... .
3x 4x
4. If −= 2 − , then x is ............... .
5
2 2
5. If 2x + 1 = –3, then x is ............... .
D. State whether the following statements are true (t) or False (F).

1. In the equation 2x – 2 = 4, transposing –2 to RHS, we get 2x = 4.
x 5
2. If = 5 , then x = .
3 3
3. If quantity a is thrice the quantity b, then 3a – b = 0.
4. We can add or subtract the same number or expression to both sides of an equation.
5. The solution of linear equation in one variable is always an integer.
E. Solve the following questions.

1. Solve the given equations.
n n 1 2m m
( a) −= + ( b) + 4 = − 1 ( c) 6x + 1 = 2x + 17
5
4 6 2 3 2
1 2t + 2 x + 1 x + 2 x + 4 1 − 9y 5
( d) 2t − − =− t ( e) + + = 3 ( f ) =
5 3 2 3 5 19 − 3y 8
2. Yanshu’s mother age is 3 times as old as Yanshu. After 6 years, her mother will be 2 times as old as
she will be then. Calculate their present ages.
3. Arvind is younger than Raj by 6 years. If ratio of their ages is 5 : 6, find the age of Arvind.
4. The sum of two numbers is 24 and their difference is 16. What will be the larger number?
5
5. A fraction is equal to . If same number is added to its numerator and denominator, then fraction
1 17
equals to . What will be the number added to this fraction?
3
6. The perimeter of rectangular board is 220 m. Its length is 2 m more than twice its breadth. What is
the length and breadth of the board?
2 2
7. The base of an isosceles triangle is cm. The perimeter of triangle is 3 cm. What is the length
of either of remaining equal sides? 3 15
8. Sam’s father is 20 years younger than Sam’s grandfather and 20 years elder than Sam. The sum of
their ages is 105 years. What is the age of each one of them?
9. Rozi has total `300 in coins of denomination `1, `2 and `5. The number of `2 coins is 3 times the
number of `5 coins. The total number of coins is 160. How many coins of each denomination are
with her?

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