Everything Maths Grade 10

SOLUTION

Step 1: Rewrite the equation

In order to get the equation into a form which we can factorise, we need to rewrite the equation:

2 x 24 x= 0

2 x 24 : 2 x= 0

2 x

24

2 x

= 0

Now eliminate the fraction by multiplying both sides of the equation by the denominator, 2 x.

(

2 x

24

2 x

)

 2 x= 0 2 x

22 x16 = 0

Step 2: Factorise the equation

Now that we have rearranged the equation, we can see that we are left with a difference of two squares.
Therefore:

22 x16 = 0

(2x4)(2x+ 4) = 0

2 x= 4 2x̸= 4 (a positive integer with an exponent is always positive)

2 x= 2^2 = 4

x= 2

Thereforex= 2.

Exercise 2 – 3:

1.Solve for the variable:

a) 2 x+5= 32 b) 52 x+2=

1

125

c) 64 y+1= 16^2 y+5 d) 39 x^2 = 27

e) 25 = 5 z^4 f)^12 : 6

m 2 +3

= 18

g) 81 k+2= 27k+4 h) 251 ^2 x 54 = 0

i) 27 x 9 x^2 = 1 j) 2 t+ 2t+2= 40

k) (7x49)(3x27) = 0 l)(2: 2 x16)(3x+19) = 0

m) (10x1)(3x81) = 0 n) 2  52 x= 5 + 5x

o) 9 m+ 3^3 ^2 m= 28 p)y 2 y

(^12)

• 1 = 0
  q) 4 x+3=0,5 r) 2 a=0,125
  Chapter 2. Exponents 55