Simple Equations
Exercise 4.3
1). Solve the following equations:
(a) 2 y + 5/2 = 37/2 (b) 5t + 28 = 10
(c) a/5 + 3 = 2 (d) q/4 + 7 = 5
(e) 5/2 x = –5 (f) 5/2 x = 25/4
(g) 7m+ 19/2 =13 (h) 6z + 10 = –2
(i) 3 l /2 =2/3 (j) 2b/3 – 5 = 3
Solution
(a) 2 y + 5/2 = 37/2
(b) 5t + 28 = 10
(c) a/5 + 3 = 2
(d) q/4 + 7 = 5
(e) 5/2 x = –5
(f) 5/2 x = 25/4
(g) 7m+ 19/2 =13
(h) 6z + 10 = –2
(i) 3 l /2 =2/3
(j) 2b/3 – 5 = 3
2). Solve the following equations:
(a) 2(x + 4) = 12 (b) 3(n – 5) = 21
(c) 3(n – 5) = – 21 (d) – 4(2 + x) = 8
(e) 4(2 – x) = 8
Solution
(a) 2(x + 4) = 12
By removing the bracket we get
2x + 8 = 12
Subtracting 8 from both the sides
2x + 8 – 8 = 12 – 8
2x = 4
Dividing both the sides by 2
2x/2 = 4/2
x = 2
(b) 3(n – 5) = 21
By removing the bracket we get
3n – 15 = 21
Adding 15 to both the sides
3n – 15 + 15 = 21 + 15
3n = 36
Dividing both the sides by 3
3n/3 = 36/3
n = 12
(c) 3(n – 5) = – 21
By removing the bracket we get
3n – 15 = -21
Adding 15 to both the sides
3n – 15 + 15 = -21 + 15
3n = -6
Dividing both the sides by 3
3n/3 = -6/3
n = -2
(d) – 4(2 + x) = 8
By removing the bracket we get
-8 – 4x = 8
Adding 8 to both the sides
-8 – 4x + 8 = 8 + 8
– 4x = 16
Dividing both the sides by 4
-4x/4 = 16/4
–x = 4
x = -4
(e) 4(2 – x) = 8
By removing the bracket we get
8 – 4x = 8
Subtracting 8 from both the sides
8 – 4x – 8 = 8 – 8
– 4x = 0
Dividing both the sides by 4
-4x/4 = 0/4
–x = 0
x = 0
3). Solve the following equations:
(a) 4 = 5(p – 2) (b) – 4 = 5(p – 2)
(c) 16 = 4 + 3(t + 2) (d) 4 + 5(p – 1) =34
(e) 0 = 16 + 4(m – 6)
Solution:
(a) 4 = 5(p – 2)
Removing brackets we have
4 = 5p – 10
Transposing -10 to LHS
4 +10 = 5p
14 = 5p
Transposing 5 to LHS
14/5 = p
p =14/5
(b) – 4 = 5(p – 2)
Removing brackets we have
-4 = 5p – 10
Transposing -10 to LHS
-4 +10 = 5p
6 = 5p
Transposing 5 to LHS
6/5 = p
p =6/5
(c) 16 = 4 + 3(t + 2)
Removing brackets we have
16 = 4 + 3t + 6
16 = 10 + 3t
Transposing 10 to LHS
16 -10 = 3t
6 = 3t
Transposing 3 to LHS
6/3 = t
2 = t
t =2
(d) 4 + 5(p – 1) =34
Removing brackets we have
4 + 5p – 5 = 34
5p – 1 = 34
Transposing -1 to RHS
5p = 34 + 1
5p = 35
Transposing 5 to RHS
p =35/5
p = 7
(e) 0 = 16 + 4(m – 6)
Removing brackets we have
0 = 16 + 4m – 24
0 = 4m – 8
Transposing -8 to LHS
0 + 8 = 4m
8 = 4m
Transposing 4 to LHS
8/4 = m
2 = m
m = 2
4). (a) Construct 3 equations starting with x = 2
x = 2
(b) Construct 3 equations starting with x = – 2
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