Exercise 12.4

1. Find the errors and correct the following mathematical sentences:

(i) 3(x – 9) = 3x – 9

Solution:

3(x - 9) = -

(ii) x(3x + 2) = 3x2 + 2

Solution:

x(3x + 2) = 3x23x +

(iii) 2x + 3x = 5x2

Solution:

2x + 3x =

(iv) 2x + x + 3x = sx

Solution:

2x + x + 3x =

(v) 4p + 3p + 2p + p – 9p = 0

Solution:

4p + 3p + 2p + p – 9p =

(vi) 3x + 2y = 6xy

Solution:

3x + 2y be simplified.

(vii) 3x2 + 4x + 7 = 3x2 + 4x + 7

Solution:

3x2 + 4x + 7 = x2 + 4x + 7

(viii) 2x2 + 5x = 4x + 5x = 9x

Solution:

2x2 + 5x = 4x24x + 5x

(ix) 2a+32 = 2a2 + 6a + 9

Solution:

2a+32 = 4a23a2 + 12a6a + 9

(x) Substitute x = –3 in

(a) x2 + 7x + 12 = −32 + 7(–3) + 12 = 9 + 4 + 12 = 25

Solution:

x2 + 7x + 12 = −32 + 7(-3) + 12

= - + =

(b) x2 – 5x + 6 = −32 – 5(–3) + 6 = 9 – 15 + 6 = 0

Solution:

x2 – 5x + 6 = −32 – 5(–3) + 6 = + + 6 =

(c) x2 + 5x = −32 + 5(–3) + 6 = –9 – 15 = –24

Solution:

x2 + 5x = −32 + 5(–3) = - =

(xi) x−42 = x2 – 16

Solution:

x−42 = x2 – +

(xii) x+72 = x2 + 49

Solution:

x+72 = x2 + + 49

(xiii) (3a + 4b)(a – b) = 3a2 – 4a2

Solution:

(3a + 4b)(a – b) = 3a2 – + – 4a2

= 3a2 + – 4a2

(xiv) (x + 4)(x + 2) = x2 + 8

Solution:

(x + 4)(x + 2) = x2 + + + 8

= x2 + + 8

(xv) (x – 4)(x – 2) = x2 – 8

Solution:

(x – 4)(x – 2) = x2 – – + 8

= x2 – + 8

(xvi) 5x3 ÷ 5x3 = 0

Solution:

5x3 ÷ 5x3 =

(xvii) 2x3 + 1 ÷ 2x3 = 1

Solution:

2x3 + 1 ÷ 2x3 = 1 + 12x32x3

(xviii) 3x + 2 ÷ 3x = 23x

Solution:

3x + 2 ÷ 3x = + 23x3x2

(xix) 3x + 5 ÷ 3 = 5

Solution:

3x + 5 ÷ 3 = +

(xx) 43 + 13 = 1

Solution:

43 + 13 =