Solve the following equations:
(i) 3x + 3 = 15
(ii) 2y + 7 = 19
(iii) 
x + 3 = 
(iv) √3x – 2 = 2√3 + 4
(v) 8u + 
= 3u +7
(vi) (√5 + 5)x + 4 = 2√5 + 8
(vii) 2x – (3x – 4) = 3x – 5
(viii) 2x + √2 = 3x – 4 – 3√2
(i) 3x + 3 = 15
3x = 15 – 3 (Transposing 3)
3x = 12
x = 12/3
... x = 4
(ii) 2y + 7 = 19
2y = 19 – 7
2y = 12 (Transposing 7)
y = 12/2
∴ y = 6
(iii)
x + 3 = 
x = – 3 (Transposing 3)
⇒ x = 
⇒x = 
⇒ x = x 
∴ x = 3
(iv) √3x – 2 = 2√3 + 4
√3x – 2 = 2√3 + 4
√3x = 2√3 + 4 + 2 (Transposing -2)
⇒ 3x = 2√3 + 6
⇒x = 2√3 + 6
√3
⇒x =
x 
⇒x =
⇒x =
⇒x =
∴ x =
(v) 8u +
= 3u + 7
⇒8u - 3u = 7 - (Transposing and 3u)
⇒5u =
⇒5u =
⇒5u =
⇒u = x 
u =
(vi) (√5 + 5)x + 4 = 2√5 + 8
(√5 + 5)x = 2√ 5 + 8 - 4 (Transposing 4)
(√5 + 5)x = 2√5 + 4
⇒x =
⇒x = x 
⇒x =
⇒x =
⇒x =
⇒x =
⇒x =
∴ x =
vii) 2x – (3x – 4) = 3x – 5
2x – 3x + 4 = 3x – 5
2x – 3x – 3x = – 5 – 4 (Transposing 4 and 3x)
– 4x = – 9
∴ x =
= 
viii) 2x + √2 = 3 x – 4 – 3√2
2x – 3x = – 4 – 3√2 – √2 (Transposing √2 and 3x)
⇒ – x = – 4 – 4√2
⇒ – x = – (4 + 4√2)
∴ x = 4 + 4√2
3x = 15 – 3 (Transposing 3)
3x = 12
x = 12/3
... x = 4
(ii) 2y + 7 = 19
2y = 19 – 7
2y = 12 (Transposing 7)
y = 12/2
∴ y = 6
(iii)
x + 3 = x = – 3 (Transposing 3)⇒
x = ⇒
x = ⇒ x =
x ∴ x = 3
(iv) √3x – 2 = 2√3 + 4
√3x – 2 = 2√3 + 4
√3x = 2√3 + 4 + 2 (Transposing -2)
⇒ 3x = 2√3 + 6
⇒x = 2√3 + 6
√3
⇒x =
x ⇒x =
⇒x =
⇒x =
∴ x =
(v) 8u +
= 3u + 7⇒8u - 3u = 7 -
(Transposing and 3u)⇒5u =
⇒5u =
⇒5u =
⇒u =
x u =
(vi) (√5 + 5)x + 4 = 2√5 + 8
(√5 + 5)x = 2√ 5 + 8 - 4 (Transposing 4)
(√5 + 5)x = 2√5 + 4
⇒x =
⇒x =
x ⇒x =
⇒x =
⇒x =
⇒x =
⇒x =
∴ x =
vii) 2x – (3x – 4) = 3x – 5
2x – 3x + 4 = 3x – 5
2x – 3x – 3x = – 5 – 4 (Transposing 4 and 3x)
– 4x = – 9
∴ x =
= viii) 2x + √2 = 3 x – 4 – 3√2
2x – 3x = – 4 – 3√2 – √2 (Transposing √2 and 3x)
⇒ – x = – 4 – 4√2
⇒ – x = – (4 + 4√2)
∴ x = 4 + 4√2
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