**Equations in One Variable – Maharashtra Board Class 7 Solutions for Mathematics (English Medium)**

MathematicsGeneral ScienceMaharashtra Board Solutions

**Exercise 38:**

**Solution 1(1):**

y – 2 = 9

[Addition Property of Equality: If the same number is added to both sides of the equality, the sums so obtained are equal.]

∴ y – 2 + 2 = 9 + 2

∴ y = 11

**Solution 1(2):**

p + 3 = 12

[Subtraction Property of Equality: If the same number is subtracted from both sides of an equality the sums so obtained are equal]

∴ p + 3 – 3 = 12 – 3

∴ p = 9

**Solution 1(3):**

**Solution 1(4):**

**Solution 1(5):**

**Solution 1(6):**

**Solution 1(7):**

**Solution 1(8):**

**Solution 1(9):**

**Solution 1(10):**

**Exercise 39:**

**Solution 1(1):**

2p = p + 7

∴ 2p – p = p + 7 – p

∴ p = 7

**Solution 1(2):**

**Solution 1(3):**

**Solution 1(4):**

4x – 5 = 3(x + 2)

∴ 4x – 5 = 3x + 6

∴ 4x – 5 – 3x = 3x + 6 – 3x

∴ x – 5 = 6

∴ x – 5 + 5 = 6 + 5

∴ x = 11

**Solution 1(5):**

**Solution 1(6):**

**Solution 1(7):**

**Solution 1(8):**

**Solution 1(9):**

**Solution 1(10):**

**Solution 1(11):**

**Solution 1(12):**

**Exercise 40:**

**Solution 1(1):**

Let x be the given number.

4 less than another number = x – 4

It is given that 4 less than one number is equal to 11.

∴ x – 4 = 11

**Solution 1(2):**

Let Soham’s age be x years.

Sagar is 2 years younger than Soham.

∴ Sagar’s age = (x – 2) years

It is given that the sum of their ages is 38.

∴ x + (x – 2) = 38

**Solution 1(3):**

Let x be the given number.

Now, twice the number = 2x

9 less than twice the number = 2x – 9

It is given that, 9 less than twice the number is 15.

∴ 2x – 9 = 15

**Solution 1(4):**

Let the breadth of the given rectangle be x cm.

So the length of the rectangle = (x + 3) cm

Perimeter of the rectangle = 2(Length + Breadth)

∴ Perimeter of the rectangle = 2(x + 3 + x)

It is given that the perimeter of the rectangle is 30 cm.

∴ 2(x + 3 + x) = 30

**Solution 1(5):**

Let x be the amount with Kiran.

∴ Amount with Sultana = x – 5

It is given that the two of them together have Rs. 51.

∴ (x – 5) + x = 51

**Exercise 41:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**