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)