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Solve the following equations.
(a) 
(b) 5t + 28 = 10 (c) 
(d) 
(e) 
(f) 
(g) 
(h) 6z + 10 = − 2 (i) 
(j) 
(a) 
(Transposing 
to R.H.S.)
Dividing both sides by 2,
(b) 5t + 28 = 10
5t = 10 − 28 = −18 (Transposing 28 to R.H.S.)
Dividing both sides by 5,
(c) 
(Transposing 3 to R.H.S.)
Multiplying both sides by 5,
a = −1 × 5 = −5
(d) 
(Transposing 7 to R.H.S.)
Multiplying both sides by 4,
q = −8
(e) 
Multiplying both sides by 2,
5x = −10 × 2 = −20
Dividing both sides by 5,
(f) 
Multiplying both sides by 2,
Dividing both sides by 5,
(g) 
(Transposing 
to R.H.S.)
Dividing both sides by 7,
(h) 6z + 10 = −2
6z = − 2 − 10 = −12 (Transposing 10 to R.H.S.)
Dividing both sides by 6,
(i) 
Multiplying both sides by 2,
Dividing both sides by 3,
(j)
(Transposing −5 to R.H.S.)
Multiplying both sides by 3,
2b = 8 × 3 = 24
Dividing both sides by 2,
b = 
= 12
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
(a) 2 (x + 4) = 12
Dividing both sides by 2,
x = 6 − 4 = 2 (Transposing 4 to R.H.S.)
(b) 3 (n − 5) = 21
Dividing both sides by 3,
n = 7 + 5 = 12 (Transposing −5 to R.H.S.)
(c) 3 (n − 5) = −21
Dividing both sides by 3,
n = − 7 + 5 = −2 (Transposing −5 to R.H.S.)
(d) −4 (2 + x) = 8
Dividing both sides by −4,
x = − 2 − 2 = −4 (Transposing 2 to R.H.S.)
(e) 4 (2 − x) = 8
Dividing both sides by 4,
2 − x = 2
−x = 2 − 2 (Transposing 2 to R.H.S.)
−x = 0
x = 0
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)
(a) 4 = 5 (p − 2)
Dividing both sides by 5,
(b) − 4 = 5 (p − 2)
Dividing both sides by 5,
(c) 16 = 4 + 3 (t + 2)
16 − 4 = 3 (t + 2) (Transposing 4 to L.H.S.)
12 = 3 (t + 2)
Dividing both sides by 3,
4 = t + 2
4 − 2 = t (Transposing 2 to L.H.S.)
2 = t
(d) 4 + 5 (p − 1) = 34
5 (p − 1) = 34 − 4 = 30 (Transposing 4 to R.H.S.)
Dividing both sides by 5,
p = 6 + 1 = 7 (Transposing −1 to R.H.S.)
(e) 0 = 16 + 4 (m − 6)
0 = 16 + 4m − 24
0 = −8 + 4m
4m = 8 (Transposing −8 to L.H.S)
Dividing both sides by 4,
m = 2
(a) Construct 3 equations starting with x = 2
(b) Construct 3 equations starting with x = − 2
(a) x = 2
Multiplying both sides by 5,
5x = 10 (i)
Subtracting 3 from both sides,
5x − 3 = 10 − 3
5 x − 3 = 7 (ii)
Dividing both sides by 2,
(b) x = −2
Subtracting 2 from both sides,
x − 2 = − 2 − 2
x − 2 = −4 (i)
Again, x = −2
Multiplying by 6,
6 × x = −2 × 6
6x = −12
Subtracting 12 from both sides,
6x − 12 = − 12 − 12
6x − 12 = −24 (ii)
Adding 24 to both sides,
6x − 12 + 24 = − 24 + 24
6x + 12 = 0 (iii)
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