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Given 3(p – 7) – 4 = 5 

⇒ 3(p – 7) – 4 + 4 = 5 + 4 (Add 4 on both sides) 

⇒ 3(p – 7) = 9

\(\frac {3(p-7)}{3} = \frac 93\) (Divide by 3 on both sides) 

⇒ p – 7 = 3 

⇒ p – 7 + 7 = 3 + 7 (Add 7 on both sides) 

⇒ p = 10 

Check: 

Substitute p = 10 in 

3(p – 7) – 4 = 5

LHS = 3(p – 7) – 4. 

= 3(10 – 7) – 4. 

= 3 × 3 – 4 

= 9 – 4 = 5 = RHS 

Hence verified.

Given – 3(m + 5) 4-1 = 13 

⇒ – 3(m + 5)+ 1 – 1 = 13 – 1 (Subtract 1 on both sides) 

⇒ – 3(m + 5) = 12

⇒ \(\frac {-3(m+5)}{-3} = \frac {12}{-3}\) (Divide by – 3 on both sides) 

⇒ m + 5 = – 4 

⇒ m + 5 – 5 = – 4 – 5 (Subtract 5 on both sides) 

⇒ m = – 9 

Check: 

Substitute m = – 9 in – 3(m + 5) + 1 = 13 

LHS = – 3(m + 5) + 1 

= – 3(- 9 + 5) + 1 

= (- 3 × – 4) + 1 

= + 12 + 1 = 13 = RHS 

Hence verified.

Given a – 2.3 = 1.5 

⇒ a – 2.3 + 2.3 = 1.5 + 2.3 (Add 2.3 ort both sides) 

⇒ a = 3.8 

Check: 

Substitute a = 3.8 in a – 2.3 =1.5 

LHS = a – 2.3 

= 3.8 – 2.3 

= 1.5 = RHS 

Hence verified.

Given 18 – 7n = – 3 

⇒ 18 – 7n – 18 = – 3 – 18 (Subtract 18 on both sides) 

⇒ – 7n = – 21

⇒ -7n/-7n = -21/-7 (Divide by – 7 on both sides)

⇒ n = 3

Check: 

Substitute n = 3 in 18 – 7n = – 3 

LHS = 18 – 7n 

= 18 – 7(3) 

= 18 – 21 

= – 3 = RHS 

Hence verified.

Given – 7m = 21

⇒ -7m/-7 = 21/-7 (Divide by – 7 on both sides)

⇒ m = – 3

Check: 

Substitute m = in – 7m = 21 

LHS = – 7m 

= – 7 (- 3) 

= 21 = RHS 

Hence verified.

Given 4p + 7 = – 21 

⇒ 4p + 7 – 7 = – 21 – 7 (Subtract 7 on both sides) 

⇒ 4p = – 28

⇒ 4p/4 = -28/4 (Divide by 4 on both sides)

⇒ p = – 7

Check:

Substitute p = – 7 in 4p + 7 = – 21 

LHS = 4p + 7 

= 4(- 7) + 7 

= – 28 + 7 

= – 21 = RHS 

Hence verified.

Given 3(k + 4) = 21 

⇒ 3k + 12 = 21 (Distributive property) 

⇒ 3k + 12 – 12 = 21 – 12 (Subtract 12 on both sides) 

⇒ 3k = 9

⇒ 3k/3 = 9/3 (Divide by 3 on both sides)

⇒ k = 3

Check: 

Substitute k = 3 in 3(k + 4) = 21 

LHS = 3(k + 4) 

= 3(3 + 4) 

= 3 × 7 = 21= RHS 

Hence verified.

Given 9(a + 1) + 2 = 11 

⇒ 9(a + 1) + 2 – 2 = 11 – 2 (Subtract 2 on both sides) 

⇒ 9(a + 1) = 9

⇒ \(\frac {9(a+1)}{9} = \frac 99\) (Divide by 9 on both sides) 

⇒ a + 1 = 1 

⇒ a + 1 – 1 = 1 – 1 (Subtract 1 on both sides) 

⇒ a = 0

Check: 

Substitute a = 0 in 9(a + 1) + 2 = 11 

LHS = 9(a + 1) + 2 

= 9(0 + 1) + 2 

= 9(1) + 2 

= 9 + 2 = 11 = RHS

Hence verified.

i) If you add 13 to 2 times of number ‘x’ is 25.

ii) 7 is subtracted from one fourth of y is 1.

Ratio of present ages of Mary and Joseph = 5:3 = 5x : 3x 

After 3 years their ages = 5x + 3 : 3x + 3 

Sum of their ages = 38 

⇒ 5x + 3 + 3x + 3 = 38 

⇒ 8x + 6 = 38

⇒ 8x + 6 – 6 = 38 – 6 (Subtract 6 on both sides) 

⇒ 8x = 32

⇒ 8x/8 = 31/8

⇒ x = 4 

⇒ Ratio of present ages = 5x : 3x 

= 5(4) : 3(4) = 20 : 12 

Present ages of Mary and Joseph are 20 years and 12 years.

Let the number be x. 

Given, six times of number = 72 

⇒ 6x = 72

⇒ 6x/6 = 72/6

⇒ x = 12 

∴ The number is 12.

Given 2n + 5 = 19 

Substitute n = 7 in the given equation 

2(7) + 5 = 19

⇒ 14 + 5 = 19 

⇒ 19 = 19 

∴ LHS = RHS 

So, n = 7 is the solution of the given equation.

Let the lowest mark = x 

then the highest mark twice the lowest mark + 7 = 93 

⇒ 2x + 7 = 93 

⇒ 2x + 7 – 7 = 93 – 7 (Subtract 7 on both side) 

⇒ 2x = 86

⇒ 2x/2 = 86/2 (Divide by 2 on both sides)

⇒ x = 43 

∴ Lowest mark = 43

Let the number be x. 

Twice the number = 2x 13 is subtracted from twice the number 

⇒ 2x- 13 = 3 

⇒ 2x – 13 + 13 = 3 + 13 (Add 13 on both sides) 

⇒ 2x = 16

⇒ 2x/2 = 16/2 (Divide 2 on both sides)

⇒ x = 8 

∴ Number is 8.

Given 2(y – 1) = 8 

⇒ 2y – 2 = 8 (Distributive property) 

⇒ 2y – 2 + 2 = 8 + 2 (Add 2 on both sides) 

⇒ 2y = 10

⇒ 2y/2 = 10/2 (Divide by 2 on both sides)

⇒ y = 5

Check: 

Substitute y = 5 in the given equation 

LHS = 2(y – 1) 

= 2(5 – 1) 

= 2 × 4 = 8 = RHS 

Hence verified.

Given – 5 + 3x = 16 

⇒ – 5 + 3x + 5 = 16 + 5 (Add 5 on both sides) 

⇒ 3x = 21

⇒ 3x/3 = 21/3 (Divide by 3 on both sides)

⇒ x = 7

Check: 

Substitute x = 7 in the given equation 

LHS = – 5 + 3x 

= – 5 + 3(7) 

= – 5 + 21 = 16 = RHS 

Hence verified.

Let one number be x. 

Other number = thrice of first number = 3(x) = 3x 

Sum of two numbers = 60 

⇒ x + 3x = 60 

⇒ 4x = 60

Let the number of white balls = x 

Number of blue balls = twice the number of white balls = 2(x) = 2x 

Number of red balls = thrice the number of blue balls = 3(2x) = 6x 

Total balls = White + Blue + Red = 27 

⇒ x + 2x + 6x = 27 ⇒ 9x = 27

⇒ 9x/9 = 27/9 (Divide by 9 on both sides)

⇒ x = 3 

Therefore white balls x = 3 

Blue balls = 2x = 2(3) = 6 

Red balls = 6x = 6(3) = 18

Given 7(x – 3) = 28 

⇒ 7x – 21 = 28 (Distributive property) 

⇒ 7x – 21 + 21 = 28 + 21 (Add 21 on both sides) 

⇒ 7x = 49

⇒ 7x/7 = 49/7 (Divide by 7 on both sides)

⇒ x = 7

(a) 7 more than twice the m is 21.

(b) One seventh of n is 4.

Let the amount spent for purchasing books for needy children = ₹ x 

Amount spent for purchasing food items for orphanage children = ₹ 3x 

Amount spent for purchasing chocolates for friends = ₹ 200 

Total amount spent = ₹ 2000

⇒ x + 3x + 200 = 2000 

⇒ 4x + 200 = 2000 

⇒ 4x = 2000 – 200 

⇒ 4x = 1800

⇒ x = 1800/4

⇒ x = 450 

∴ Amount spent for purchasing books for needy children = ₹ 450 

Amount spent for purchasing food items for orphanage children = ₹ 3x 

= 3 × 450 = ₹ 1350 

Check: 

Amount = ₹ 450 + ₹ 1350 + ₹ 200 

= ₹ 2000 

Hence Verified.

Let the number = m 

4 times the number = 4m

By decreasing 3 the result = 4m – 3 

∴ 4m – 3 = 5

Given number = x 

Five times of a number = 5 ∙ x 

By adding 3 the result = 5x + 3 

∴ 5x + 3 = 28

Let the breadth of the rectangle = x, 

length of a rectangle is five more than twice of its breadth. 

Then, length of the rectangle = 2x + 5 

Perimeter of the rectangle = 148m 2 (Length + Breadth) = 148 

⇒ 2(2x + 5 + x) = 148 

⇒ 2(3x + 5) = 148

⇒ 6x + 10 = 148 

⇒ 6x = 148 – 10 

⇒ 6x = 138

⇒ x = 138/6

⇒ x = 23 

∴ Breadth of rectangle = 23 m 

Length of the rectangle = 2x + 5 = (2 × 23) + 5 

= 46 + 5 = 51 m 

Check: 

Length = 51 m, Breadth = 23 m 

Perimeter = 2(l + b) 

= 2(51 + 23) 

= 2(74) 

= 148 m 

Hence Verified.

Breadth of rectangle = x 

Length of rectangle = x + 3 

Perimeter = 2(x + 3 + x) = 4x + 6 

Given Perimeter = 24 m 

∴ 4x + 6 = 24