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CANADIAN MATHEMATICS 8
6.3 SOLVING TYPE III EQUATIONS
, A Type III equation is one where there is more than one group of variables (letters). To solve aType III equation you should first collect and place all the variables (letters) on the left side of the
equal sign or equation, and all the constants (numbers) on the right side of the equal sign or
equation by using opposite operations. That means if an 'x' term is on the right side of the equal
sign, bring it over to the left side by using the opposite sign. Likewise, if a number is being added
or subtracted on the left side of an equation, bring it over to the right side by using the opposite
sign as shown in the two examples below.
EXAMPLE #1
EXAMPLE #2
5x - 3 = 3x + 14
5x -3x = 14 + 3
2x = 17
2x = 17
2
2
x=8.5
6x - 4.3 + 3x = 86.2 - lx
6x + 3x + lx = 86.2 + 4.3
10x = 90,5
10x = 90.5
10
10
x = 9.05
A. Solve the following.
1. 3x + 8x = 44
2. 7x - 3x = 44
3. -2x - 8x = -100
4. 1/ 3 y + 2/ 3 y = 14
5. -3.2a + 5a = 90
6. 12 = 3/ 4 x + 5/ 4 x
7. 7x -5x ---- -20
8. 3x - 10x = 15
9. 4x + 3.2x= 18
10. 7x + 6 = 12
11. 5x - 3 = 2x + 8
.12.
14. 4x + 3 = 9x + 7 ,
15. 1/ 2 x + 2 = 3/ 4 x + 7
16. 0.4x + 8 = 0.6x - 7
17. 6x + 1.2 = 9x + 2
18. 6/ x - 2 = 2/ 7 x + 8
19.
+ 20 = x + 4
20. 1/ 2 a + 9 = 2a - 6
21. 0.02x + 7 = 0.03x + 5
22. 5x - 10 = 25x + 3
23. 7x - 10 = 3x + 14
24. 0.1y + 0.01 = 0.01y + 0.1
25. 3x ± 10 + 5x = 90
26. 6 -5 -2x = 7 + 1 27. 16 ±45x = 39x + 310
28. 7x - 3 - 2x = 8
29. 8x + 4x + 5x = 7
71.
,R7A
4.0
13.
-2/ 3
x+5=7
3X
EQUATIONS AND INEQUALITIES
-5x -
= -2x + 8
30. 2x - 3 = 6x + 4x
75
CANADIAN MATHEMATICS 8
B. Extra Practice. Solve the following.
1. 3x + 6x = 81
2. 3x + 6 = 2x + 5
kir0/
4. 617 x - 2 = 2/ 7 x + 8 5. 6x + 1.2 = 9x + 2
7. 64 = -3x - 5x
3. 32 + 90x = 78x + 620
8. 5x - 3 = 2x + 8
6. 2x + 5 - 3x + 8 = 7
9. 6x + bx + 360 = 600
10. 12 - 8y = 5y - 14
11. -3x + 7 = 3x - 17
12. x + 3 + x + 8 = 22
13. 5x = 4x
14. 12x + 13x = 50
15. -3x + 2x - 6x = 49
16. -5x•- = -2x + 8
17. 4x + 3 = 9x + 7
18. 3x - 8 = 7x + 5
19. 8x - 9 = 25 -
20. x + 2x + 3x = 30
21. x + x + 4 + x + 8 = 96
22. 60 + 3x = 200 - 2x 23. 5x - 3 = 2x + 8 . 24. 1/ 2 X + 2 = 3/ 4 x - 7
25. 4x = 3x + 2x - 5
26. 3x - x = 16
27. 9y + 45 = -ly + 135
28. 4x - x + 7x = 15
29. 7x - 8= 3x + 5
30. 0.4x + 8 = 0.6x - 8
31. 0.3x - 4 = 0.6x - 8
32. 3x = 5x + 6
33. 5x + 100 - 2.5x = 165
34. 0.5x + 9 = 2x - 6
35. 1/ 3 x + 20 = x + 4
36. 7.2x + 9 = 5.2x - 8
37. 7x + 8 = 6x
38. 2x - 8 = 3x + 5
39. 0.3x + 1.6 = 0.4x + 1.9
40. 5x + 3 = 4x + 3
41. 7x -
42. 1/ 2 X - 8 = 1/ 4 X + 3
= 67 + 33
43. 8x + 3x + 5x = -256 44. 1/ 2 X+ / 3 x = 12
46. 14x + 12 = 24
47. 9x -30x = 45
_ 45 4x
= 12x + 8x
48. 14x -6x -4x = 16
va;
{.76
I
CHAPTER
CANADIAN MATHEMATICS 8
6.3 SOLVING TYPE III EQUATIONS
A Type III equation is one where there is more than one group of variables (letters). To solve a
TypOI equation you should first collect and place all the variables (letters) on the left side of the
equal lign or equation, and all the constants (numbers) on the right side of the equal sign or
equation by using opposite operations. That means if an 'x' term is on the right side of the equal
sign, bring it over to the left side by using the opposite sign. Likewise, if a number is being added
or subtracted on the left side of an equation, bring it over to the right side by using the opposite
sign as shown in the two examples below.
EXAMPLE #2
EXAMPLE #1
6x - 4.3 + 3x = 86.2 - lx
6x + 3x + lx = 86.2 + 4.3
10x = 90.5
10x = 90.5
10
10
x =9.05 .
5x - 3 = 3x + 14
5x -3x = 14 + 3
2x = 17
2x = 17
2
2
x
8.5
A. Solve the following.
1. 3x + 8x = 44
j1
Li
3
y + 2/ 3 y = 14
10. 7x + 6 = 12
c.
-3
(c)
8. 3x - 10x = 15
_L
11. 5x - 3 = 2x + 8
c2.5
12. -5x - 3 = -2x + 8
3I
14. 4x + 3 = 9x + 7
.
-
-3 _2315. 1/ 2 x + 2 = 3/ 4 x + 7
-a0
5"
- 0 . a to
19. 1/ 3 x + 20 = x + 4
;1/49
20. 1/ 2 a + 9 = 2a - 6
22. 5x -10 = 25x + 3
23. 7x -10 = 3x +14
-13
9. 4x + 3.2x = 18
- a -)
16. 0.4x + 8 = 0.6x - 7 17. 6x + 1.2 = 9x± 2
-75
6. 12 = 3/ 4 x + 5/ 4 x
5D
--:1
13. -2/ 3 x + 5 = 7
-10
5. -3.2a + 5a = 90
/ Li
7. 7x - 5x = -20
. -ID
3. -2x - 8x = -100
2. 7x - 3x = 44
/0
6
18.
-2 = 2/ 7 x + 8
/7
-5
21. 0.02x + 7 = 0.03x + 5
aD 0
24. 0.1y + 0.01 = 0.01y + 0.1
i
.a.c.
25. 3x +•10 + 5x = 90
10
26. 6x -5 -2x = 7 + 1 27. 16 + 45x = 39x -i- 310
28. 7x - 3 - 2x = 8
29. 8x + 4x.+ 5x =7
3-a5"
-7
EQUATIONS AND INEQUALITIES
30. 2x -3 = 6x + 4x
4
CANADIAN MATHEMATICS 8
4
4
4
B. Extra Practice. Solve the following.
1. 3x + 6x = 81
2. 3x + 6 = 2x + 5
,
Li
-I
,
3. 32 + 90x = 78x + 620
4. 617 x - 2 = 2/ 7 x + 8 5. 6x + 1.2 = 9x + 2
6. 2x + 5 - 3x + 8 = 7
17.5
7. 64 = -3x -5x
8. 5x -3 = 2x + 8
‘,
4
4
4
9. 6x + 6x + 360 = 600
10. 12 - 8y = 5y - 14
11. -3x + 7 = 3x - 17
a
5.6
14. 12x + 13x = 50
13. 5x = 4x
0
12. x + 3 + x + 8 = 22
,.
a
15. -3x + 2x - bx = 49
-i
16. -5x - 3 = -2x + 8
17. 4x + 3 = 9x + 7
18. 3x - 8 = 7x + 5
19. 8x - 9 = 25 - 9x
20. x + 2x + 3x = 30
21. x + x + 4 + x + 8 = 96
22. 60 + 3x.= 200 - 2x 23. 5x - 3 = 2x + 8
25. 4x = 3x + 2x -5
26. 3x - x = 16
_.1._
- 3 if
24. "2 X + 2 = 3/ 4 x - 7
3(
27. 9y + 45 = -1y + 135
1
5
28. 4x - x + 7x = 15
29. 7x - 8 = 3x + 5
30. 0.4x + 8 = 0.6x - 8
31. 0.3x - 4 = 0.6x - 8
32. 3x = 5x + 6
33. 5x + 100 - 2.5x = 165
/3:11
-3
35. 1/ 3 x + 2,0 = x + 4
36. 7.2x + 9 = 5.2x - 8
37. 7x + 8 = 6x
38. 2x - 8 = 3x + 5
39. 0.3x + 1.6 = 0.4x+ 1.9
40. 5x + 3 = 4x + 3
0
-13
41. 7x - 5x = 67 + 33
50
43. 8x + 3x + 5x = -256 44. 1/ 2 x +/ 3 x = 12
-16
46. 14x + 12 = 24
6
----
/1.14
47. 9x - 30x = 45
1
- /
4
4
4
4
4
ca6
34. 0.5x + 9 = 2x - 6
/ 0
-8
4
4
4
4
4
4
-3
42. 112 x - 8 = 1/ 4 x + 3
44
45. 4x -6 = 12x + 8x
__ 3
?
48 14x - 6x - 4x = 16
LI
CHAPTER 6
4
4
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