1. Solve the following equations:
(a) 2y + (5/2) = (37/2)
Solution:
Transposing (5/2) from LHS to RHS, then it becomes (-5/2)
2y = (37/2) – (5/2)
2y = (37-5)/2
2y = 32/2
2y = 16
Dividing both side by 2,
2y/2 = (16/2)
y = (16/2)
y = 8
(b) 5t + 28 = 10
Solution:
Transposing 28 from LHS to RHS, then it becomes (-28)
5t = 10 – 28
5t = – 18
Dividing both side by 5,
5t/5= -18/5
t = -18/5
(c) (a/5) + 3 = 2
Solution:
Transposing 3 from LHS to RHS, then it becomes (-3)
a/5 = 2 – 3
a/5 = – 1
Multiplying both side by 5,
(a/5) × 5= -1 × 5
a = -5
(d) (q/4) + 7 = 5
Solution:
Transposing 7 from LHS to RHS, then it becomes -7
q/4 = 5 – 7
q/4 = – 2
Multiplying both side by 4,
(q/4) × 4= -2 × 4
a = -8
(e) (5/2) x = -5
Solution:
Multiplying both the side by 2,
(5x/2) × 2 = – 5 × 2
5x = – 10
Dividing both the side by 5,
we get,
5x/5 = -10/5
x = -2
(f) (5/2) x = 25/4
Solution:
Multiplying both the side by 2,
(5x/2) × 2 = (25/4) × 2
5x = (25/2)
Dividing both the side by 5,
we get,
5x/5 = (25/2)/5
x = (25/2) × (1/5)
x = (5/2)
(g) 7m + (19/2) = 13
Solution:
Transposing (19/2) from LHS to RHS it becomes -19/2
Now,
7m = 13 – (19/2)
7m = (26 – 19)/2
7m = 7/2
Dividing both side by 7,
7m/7 = (7/2)/7
m = (7/2) × (1/7)
m = ½
(h) 6z + 10 = – 2
Solution:
Transposing 10 from LHS to RHS it becomes – 10
Now,
6z = -2 – 10
6z = – 12
Dividing both side by 6,
6z/6 = -12/6
m = – 2
(i) (3/2) l = 2/3
Solution:
Multiplying both the side by 2,
(3l/2) × 2 = (2/3) × 2
3l = (4/3)
Dividing both the side by 3,
we get,
3l/3 = (4/3)/3
l = (4/3) × (1/3)
x = (4/9)
(j) (2b/3) – 5 = 3
Solution:
Transposing -5 from LHS to RHS it becomes 5
Now,
2b/3 = 3 + 5
2b/3 = 8
Multiplying both side by 3,
(2b/3) × 3= 8 × 3
2b = 24
Divide both side by 2,
2b/2 = 24/2
b = 12
2. Solve the following equations:
(a) 2(x + 4) = 12
Solution:
Let us divide both the side by 2,
(2(x + 4))/2 = 12/2
x + 4 = 6
By transposing 4 from LHS to RHS it becomes -4
x = 6 – 4
x = 2
(b) 3(n – 5) = 21
Solution:
Let us divide both the side by 3,
(3(n – 5))/3 = 21/3
n – 5 = 7
By transposing -5 from LHS to RHS it becomes 5
n = 7 + 5
n = 12
(c) 3(n – 5) = – 21
Solution:
Let us divide both the side by 3,
(3(n – 5))/3 = – 21/3
n – 5 = -7
By transposing -5 from LHS to RHS it becomes 5
n = – 7 + 5
n = – 2
(d) – 4(2 + x) = 8
Solution:
Let us divide both the side by -4,
(-4(2 + x))/ (-4) = 8/ (-4)
2 + x = -2
By transposing 2 from LHS to RHS it becomes – 2
x = -2 – 2
x = – 4
(e) 4(2 – x) = 8
Solution:
Let us divide both the side by 4,
(4(2 – x))/ 4 = 8/ 4
2 – x = 2
By transposing 2 from LHS to RHS it becomes – 2
– x = 2 – 2
– x = 0
x = 0
3. Solve the following equations:
(a) 4 = 5(p – 2)
Solution:
Dividing both the side by 5,
4/5 = (5(p – 2))/5
4/5 = p -2
Transposing (– 2) from RHS to LHS it becomes (2)
(4/5) + 2 = p
(4 + 10)/ 5 = p
p = 14/5
(b) – 4 = 5(p – 2)
Solution:
Let us divide both the side by 5,
– 4/5 = (5(p – 2))/5
– 4/5 = p -2
Transposing – 2 from RHS to LHS it becomes 2
– (4/5) + 2 = p
(- 4 + 10)/ 5 = p
p = 6/5
(c) 16 = 4 + 3(t + 2)
Solution:
Transposing (4) from RHS to LHS it becomes (– 4)
16 – 4 = 3(t + 2)
12 = 3(t + 2)
Divide both the side by 3,
12/3 = (3(t + 2))/ 3
4 = t + 2
Transposing 2 from RHS to LHS it becomes – 2
4 – 2 = t
t = 2
(d) 4 + 5(p – 1) =34
Solution:
Transposing 4 from LHS to RHS it becomes – 4
5(p – 1) = 34 – 4
5(p – 1) = 30
Divide both the side by 5,
(5(p – 1))/ 5 = 30/5
p – 1 = 6
Transposing – 1 from RHS to LHS it becomes 1
p = 6 + 1
p = 7
(e) 0 = 16 + 4(m – 6)
Solution:
Transposing 16 from RHS to LHS it becomes – 16
0 – 16 = 4(m – 6)
– 16 = 4(m – 6)
Divide both the side by 4,
– 16/4 = (4(m – 6))/ 4
– 4 = m – 6
Transposing – 6 from RHS to LHS it becomes 6
– 4 + 6 = m
m = 2
4. (a) Construct 3 equations starting with x = 2
Solution:
First equation is,
X = 2
Multiplying both side by 6
6x = 12 … (equation 1)
Second equation is,
6x = 12
Subtracting 4 from both side,
6x – 4 = 12 -4
6x – 4 = 8 … (equation 2)
Third equation is,
6x – 4 = 8
Dividing both side by 6
(6x/6) – (4/6) = (8/6)
x – (4/6) = (8/6) … (equation 3)
(b) Construct 3 equations starting with x = – 2
Solution:
First equation is,
X = -10
Multiply both side by 5
5x = -10 … (equation 1)
Second equation is,
5x = -10
Subtracting 3 from both side,
5x – 3 = – 10 – 3
5x – 3 = – 13 … (equation 2)
Third equation is,
5x – 3 = -13
Dividing both sides by 2
(5x/2) – (3/2) = (-13/2) … (equation 3)
👍👍👍
