Equations with variables on both sides

1.    7v = 45 + 2v

2.    12 - 3r = 3r

3.    4x + 18 = 10x

4.    4z + 2 = 2z + 8

5.    4r + 2 = 2r + 2

6.    5w + 2 = w + 7

7.    7f - 1 = 29 + f

8.    24x - 24 = 12 + 2x

9.    6 + 4(2 - t) = 3t

10.  7m + 5(3 - m) = 19

11.  12( x/3 - 1/2) = x + 21

12.  4/5 (a + 10) = a

13.  3t + 4 = 3( t + 2)

14.  5 - b = b + 5

15.  4(k + 1) + 9 = 2(3k - 4) + k

16.  5(2y + 3) - 4y = 3(2 + y) + 39

17.  2/5 (x + 1) + 3/5 (x + 1) = 14

18.  2(t + 4) - 3 = 1/2 (10 + 4t)

19.  7m - 4 - m = 31 + 2m - 5

20.  3(2t -5) - 7 = 9t - 4

21.  3/4 (5y -4) = 13 + 1/4 (6y + 8)

22.  12 + 3(2k - 1) = 2(3k + 1)

23.  Find a number such that the difference of twice the number and two-thirds of the number is 68.

24.  The sum of two numbers is 20.  Four times the larger is 1 less than five times the smaller.  Find the numbers.
 
 
 
 
 
 

ANSWERS:

1.  v = 9

2.  r = 2

3.  x = 3

4.  z = 3

5.  r = 0

6.  w = 5/4

7.  f = 5

8.  x = 18/11

9.  t = 2

10.  m = 2

11.  x = 9

12.  a = 40

13.  no solution

14.  b = 0

15.  k = 7

16.  y = 10

17.  x = 13

18.  identity   t = all real numbers

19.  m = 7 1/2  (or 7.5   or 15/2)

20.  t = -6

21.  y = 8

22.  no solution

23.  n = 51

24.  9 and  11
 
 

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