h.hofstede (h.hofstede@hogeland.nl)

       
1. a. 2x 4  =  2/2x 
2x 22 = 21 2-x
2x + 2 = 21 - x
x +
2 = 1 - x
2x  = -1
x = -1/2
 
       
  b. 3x 34 = 1
3x + 4 = 30 
x + 4 = 0
x = -4
 
       
  c. 5x 5-1 = 1/125
5x - 1 = 1/53
5x - 1 = 5-3
x - 1 = -3
x = -2
 
       
  d. 3/(32x + 1) = 27 
3 3-(2x + 1) = 33
31 - 2x - 1 = 33
-2x = 3
x = -11/2
 
       
  e. (2-2)-2 = 32 2x
2-2-2 = 25  2x
24 = 25 + x
4 = 5 + x
x
= -1
 
       
  f. 16 4x = 64/42x
42 4x = 43  4-2x
42 + x =  43 - 2x
2 + x = 3 - 2x
3x = 1
x = 1/3
 
       
  g. 2/2x = 16x
23  2-x = (24)x
23 - x  = 24x
3 - x = 4x
3 = 5x
x
=
3/5
 
       
  h. 2x + 2x  = 218
2 2x = 218
21 + x = 218
1 + x = 18
x = 17
 
       
  i. 1 =  4/(2-x+ 3)
20 = 22 2-(-x + 3)
20 = 22 2x - 3
20 = 22 + x - 3
0 = 2 + x- 3
x = 1
 
       
  j. 32 x5  = (x + 1)5
25 x5 = (x + 1)5
(2x)5 = (x + 1)5
2x = x + 1
x = 1
 
       
2. a. x-3 x4 = x-3 + 4 = x-1  
       
  b. x/x-5  =  x2 x - -5 = x2 + 5 = x7    
       
  c. 1/x5 1/x-3 x-5 x - -3 = x-5 + 3 = x-2  
       
  d. x5   1/x = x5 x-8 = x5 - 8 = x-3  
       
  e. x2 1/ =  x2 x-1  = x2 - 1 = x1 = x   
       
  f. x x2 x-6 = x1 x2 x -6  = x 1 + 2 - 6 = x-3  
       
  g.  x3 (x6)-2 = x3 x12 = x15  
       
  h. (x-2)4 1/x-2 = x-8 x - -2 = x-8 + 2 = x-6  
       
  i.  (x/x)5 = (x x-2 )5 = (x1-2)5 = (x-1)5 = x-1 5 = x-5   
       
3. a. 5p-2 q3 = 5 1/p q3  = 5q/p  
       
  b. 1/8x-1 = 1/8 1/x = 1/(8x)  
       
  c. (2x)-3 1/x = 1/(2x) 1/x  =  1/8x 1/x = 1/(8xx) = 1/8x4  
       
  d. (2/3)-2 = 1/(2/3) = 1/(4/9) = 9/4  
       
  e. (1/x-2 )5 = (x2 )5 = x10  
       
  f. 2/b-2 (1/b)2 = 2b2 (b-1)2  = 2b2 b-2  = 2b2 - 2 = 2b0 = 2 1 = 2  
       
4. R2 - S2 =  (3x + 3-x)2  - (3x - 3-x)
= (3x)2 + 2 3x 3-x + (3-x)2 - (3x)2 + 2 3x 3-x - (3-x)2
=  2 3x 3-x  + 2 3x 3-x
=
4 3x 3-x
= 4 30
= 4
       
       

h.hofstede (h.hofstede@hogeland.nl)