**1) Solve the following equations:**

**a) 2y + 5/2 = 37/2**

**Ans:** 2y = 37/2 – 5/2

→ 2y = (37-5)/2

→ 2y = 32/2

→ 2y = 16

→ y = 16/2

→ y =8

**b) 5t + 28 = 0**

**Ans**: 5t = 10 – 28

→ 5t= -18

→ t = (-18)/5

**c) a/5 + 3 = 2**

**Ans:** a/5 = 2 – 3

→ a/5 = -1

→ a = -1 x 5

→ a = -5

**d) q/4 + 7 = 5**

**Ans:** q/4 = 5 – 7

→ q/4 = -2

→ q = -2 x 4

→ q = -8

**e) 5x/2 = 10**

**Ans:** 5x = 10 x 2

→ 5x = 20

→ x = 20/5

→ x = 4

**f) 5x/2 = 25/4**

Ans: 5x = 25/4 x 2

→ 5x = 25/2

→ x = 25/(2 x 5)

→ x = 4

**g) 7m + 19/2 = 13**

**Ans**: 7m = 13 – 19/2

→ 7m = (13 x 2)/(1 x 2) – (19 x 1 )/(2 x 1)

→ 7m = (26-19)/2

→ 7m = 7/2

→ m = 7/(7 x 2)

→ m = 1/2

**h) 6z + 10 = -2**

**Ans:** 6z = -2 -10

→ 6z = -12

→ z = (-12)/6

→ z = -2

**i) 3l/2 = 2/3**

**Ans:** 3l = 2/3 x 2

→ 3l = 4/3

→ l = 4/(4 x 3)

→ l = 4/9

**j) 2b/3 – 5 = 3**

**Ans:** 2b/(3 ) = 3 + 5

→ 2b/3 = 8

→ 2b = 8 x 3

→ 2b = 24

→ b = 24/2

→ b = 12

**2) Solve the following equations:**

**a) 2( x + 4) = 12**

**Ans:** Dividing both sides by 2

(2 ( x+4 ))/2 = 12/2

→ x + 4 = 6

→ x = 6 – 4

→ x = 2

**b) 3(n – 2) = 21**

**Ans:** Dividing both sides by 3

(3(n-5))/3 = 21/3

→ n – 5 = 7

→ n = 7 – 5

→ n = 12

**c) 3(n – 5) = -21**

**Ans:** Dividing both sides by 3

(3( n-5))/3 = (-21)/3

→ n – 5 = -7

→ n = -7 + 5

→ n = -2

**d) -4 (2 + x ) = 8**

**Ans:** Dividing both sides by -4

(-4 ( 2+x))/(-4) = 8/(-4)

→ 2 + x = -2

→ x = -2 – 2

→ x = – 4

**e) 4(2 – x ) = 8**

**Ans:** Dividing both sides by 4

(4 (2-x))/4 = 8/4

→ 2 – x = 2

→ – x = – 2 – 2

→ – x = 0

→ x = 0

**3) Solve the following equations:**

**4 = 5( p – 2)**

**Ans:** Dividing both sides by 5

4/5 = (5 ( p-2))/5

→ 4/5 = p – 2

→ 4/5 + 2 = p

→ (4+10)/5 = p

→ p = 14/5

**b)– 4 = 5 ( p – 2 )**

**Ans:** Dividing both sides by 5

(- 4)/5 = (5 ( p-2 ))/5

→ (-4)/5 = p – 2

→ (- 4)/5 + 2 = p

→ (- 4+10)/(5 ) = p

→ p = 6/5

**c) 16 = 4 + 3 ( t + 2 )**

**Ans:** 16 – 4 = 3 ( t + 2 )

→ 12 = 3 ( t + 2 )

Dividing both sides by 3

12/3 = (3 ( t+2 ))/3

→ 4 = t + 2

→ t = 4 – 2

→ t = 2

**d) 4 + 5 ( p – 1 ) = 34**

**Ans:** 5 ( p – 1 ) = 34 – 4

→ 5 ( p – 1 ) = 30

Dividing both sides by 5

(5 ( p-1 ))/5 = 30/5

→ p – 1 = 6

→ p = 6 + 1

→ p = 7

**e) 0 = 16 + 4 ( m – 6 )**

**Ans:** 0 – 16 = 4 ( m – 6 )

→ – 16 = 4 ( m – 6 )

Dividing both sides by 4

(- 16)/(4 ) = (4 ( m-6 ))/4

→ – 4 = m – 6

→ – 4 + 6 = m

→ m = 2

**4) Incomplete**

**a) Construct 3 equations starting with x = 2**

**Ans:** x = 2

Multiplying both sides by 4

4x = 8 —– (eq. 1)

Adding 2 on both sides

4x + 2 = 8 + 2

4x + 2 = 10 ——– (eq. 2)

Dividing by 2 on both sides

4x/(2 ) + 2/2 = 10/2

2x + 1 = 5 —— (eq. 3)

**b) Construct 3 equations starting with x = -2**

**Ans:** x = -2

Multiplying both sides by 6

6x = -2 x 6 → 6x = -12 —– (eq. 1)

Adding 4 on both sides

6x + 4 = -12 + 4 → 6x + 4 = -8 —– (eq. 2)

Dividing by 2 on both sides

6x/2 + 4/2 = (-8)/2

3x + 2 = -4 ——- (eq. 3)