Contents

**Equations with One Variable – Maharashtra Board Class 6 Solutions for Mathematics (English Medium)**

MathematicsGeneral ScienceMaharashtra Board Solutions

### Exercise-58

**Solution 1:**

### Exercise-59

**Solution 1:**

### Exercise-60

**Solution 1:**

- Equation.
- Equation.
- Equality.
- Equation.
- Equation.
- Equality.

### Exercise-61

**Solution 1:**

### Exercise-62

**Solution 1(1):**

Let us see, for which value of x, the value of 7x becomes 14.

When x = 1, 7x = 7 × 1 = 7

When x = 2, 7x = 7 × 2 = 14

∴ The solution of the equation 7x = 14 is 2.

**Solution 1(2):**

Let us see, for which value of x, the value of x – 10 becomes 2.

When x = 11, 11 – 10 = 1

When x = 12, 12 – 10 = 2

∴ The solution of the equation x – 10 = 2 is 12.

**Solution 1(3):**

Let us see, for which value of p, the value of p + 6 becomes 10.

When p = 1, p + 6 = 1 + 6 = 7

When p = 2, p + 6 = 2 + 6 = 8

When p = 3, p + 6 = 3 + 6 = 9

When p = 4, p + 6 = 4 + 6 = 10

∴ The solution of the equation p + 6 = 10 is 4.

**Solution 1(4):**

Let us see, for which value of p, the value of 7 – p becomes 5.

When p = 1, 7 – p = 7 – 1 = 6

When p = 2, 7 – p = 7 – 2 = 5

∴ The solution of the equation 5 = 7 – p is 2.

**Solution 1(5):**

Let us see, for which value of p, the value of 13 + y becomes 18.

When y = 3, 13 + y = 13 + 3 = 16

When y = 4, 13 + y = 13 + 4 = 17

When y = 5, 13 + y = 13 + 5 = 18

∴ The solution of the equation 13 + y = 18 is 5.

**Solution 1(6):**

**Solution 1(7):**

**Solution 1(8):**

Let us see, for which value of p, the value of 2m becomes 16.

When m = 6, 2m = 2 × 6 = 12

When m = 7, 2m = 2 × 7 = 14

When m = 8, 2m = 2 × 8 = 16

∴ The solution of the equation 16 = 2m is 8.

**Solution 1(9):**

**Solution 1(10):**

Let us see, for which value of n, the value of 2 + n becomes 8.

When n = 4, 2 + n = 2 + 4 = 6

When n = 5, 2 + n = 2 + 5 = 7

When n = 6, 2 + n = 2 + 6 = 8

∴ The solution of the equation 2 + n = 8 is 6.

**Solution 1(11):**

Let us see, for which value of x, the value of 9 – x becomes 6.

When x = 1, 9 – x = 9 – 1 = 4

When x = 2, 9 – x = 9 – 2 = 5

When x = 3, 9 – x = 9 – 3 = 6

∴ The solution of the equation 9 – x = 6 is 3.

**Solution 1(12):**

Let us see, for which value of y, the value of y – 4 becomes 0.

When y = 1, y – 4 = 1 – 4 = -3

When y = 2, y – 4 = 2 – 4 = -2

When y = 3, y – 4 = 3 – 4 = -1

When y = 4, y – 4 = 4 – 4 = 0

∴ The solution of the equation y – 4 = 0 is 4.

### Exercise-63

**Solution 1(1):**

m – 4 = 1

∴ m – 4 + 4 = 1 + 4 (Addition property of equality)

∴ m + 0 = 5 [∵(-5) + 5 = 0 and 4 +1 = 5]

∴ m = 5 (∵ Any number + 0 = the same number.)

When the value of m is 5, the two sides of the equation become equal.

∴ 5 is the solution of the given equation.

**Solution 1(2):**

p + 4 = 11

∴ p + 4 – 4 = 11 – 4 (Subtraction property of equality)

∴ p + 0 = 7 [∵(-4) + 4 = 0 and 11 – 4 = 7]

∴ p = 7 (∵ Any number + 0 = the same)

When the value of p is 7, the two sides of the equation become equal.

∴ 7 is the solution of the given equation.

**Solution 1(3):**

**Solution 1(4):**

**Solution 1(5):**

6 = k – 2

∴ 6 + 2 = k – 2 + 2 (Addition property of equality)

∴ 8 = k + 0 [∵(-2) + 2 = 0 and 6 + 2 = 8]

∴ 8 = k (∵ Any number + 0 = the same)

When the value of k is 8, the two sides of the equation become equal.

∴ 8 is the solution of the given equation.

**Solution 1(6):**

25 = t + 16

∴ 25 – 16 = t + 16 – 16 (Subtraction property of equality)

∵ 9 = t + 0 [∵(-16) + 16 = 0 and 25 – 16 = 9]

∵ 9 = t (∵ Any number + 0 = the same)

When the value of t is 9, the two sides of the equation become equal.

∴ 9 is the solution of the given equation.

**Solution 1(7):**

**Solution 1(8):**

**Solution 1(9):**

8 = z + 5

∵ 8 – 5 = z + 5 – 5 (Subtraction property of equality)

∵ 3 = z + 0 [∵(-5) + 5 = 0 and 8 – 5 = 3]

∵ 3 = z (∵ Any number + 0 = the same number)

When the value of z is 3, the two sides of the equation become equal.

∴ 3 is the solution of the given equation.

**Solution 1(10):**

n – 6 = 6

∴ n – 6 + 6 = 6 + 6 (Addition property of equality)

∴ n + 0 = 12 [∵(-6) + 6 = 0 and 6 + 6 = 12]

∴ n = 12 (∵ Any number + 0 = the same number)

When the value of n is 12, the two sides of the equation become equal.

∴ 12 is the solution of the given equation.

**Solution 1(11):**

**Solution 1(12):**