Exercise algebra.equations.linear.balance

Description
Solve a linear equation using only balance rules.

Derivations

1.

5*x+3 == 18

⇒ algebra.equations.linear.balance.con-right-minus, term=3

5*x == 15

⇒ algebra.equations.linear.balance.scale-to-one, factor=5

x == 3

2.

11*x-12 == 21

⇒ algebra.equations.linear.balance.con-right-plus, term=12

11*x == 33

⇒ algebra.equations.linear.balance.scale-to-one, factor=11

x == 3

3.

19-3*x == -5

⇒ algebra.equations.linear.balance.con-right-minus, term=19

-3*x == -24

⇒ algebra.equations.linear.balance.scale-to-one, factor=-3

x == 8

4.

-12+5*x == 33

⇒ algebra.equations.linear.balance.con-right-plus, term=12

5*x == 45

⇒ algebra.equations.linear.balance.scale-to-one, factor=5

x == 9

5.

15-9*x == 6

⇒ algebra.equations.linear.balance.con-right-minus, term=15

-9*x == -9

⇒ algebra.equations.linear.balance.scale-to-one, factor=-9

x == 1

6.

4*x+18 == 0

⇒ algebra.equations.linear.balance.con-right-minus, term=18

4*x == -18

⇒ algebra.equations.linear.balance.scale-to-one, factor=4

x == -9/2

7.

11*x-12 == -34

⇒ algebra.equations.linear.balance.con-right-plus, term=12

11*x == -22

⇒ algebra.equations.linear.balance.scale-to-one, factor=11

x == -2

8.

-2*x-3 == -4

⇒ algebra.equations.linear.balance.con-right-plus, term=3

-2*x == -1

⇒ algebra.equations.linear.balance.scale-to-one, factor=-2

x == 1/2

9.

6*x-12 == 2

⇒ algebra.equations.linear.balance.con-right-plus, term=12

6*x == 14

⇒ algebra.equations.linear.balance.scale-to-one, factor=6

x == 7/3

10.

-4*x-13 == -11

⇒ algebra.equations.linear.balance.con-right-plus, term=13

-4*x == 2

⇒ algebra.equations.linear.balance.scale-to-one, factor=-4

x == -1/2

11.

6*x-2 == 2*x+14

⇒ algebra.equations.linear.balance.var-left-minus, term=2*x

4*x-2 == 14

⇒ algebra.equations.linear.balance.con-right-plus, term=2

4*x == 16

⇒ algebra.equations.linear.balance.scale-to-one, factor=4

x == 4

12.

3+6*x == 3*x+24

⇒ algebra.equations.linear.balance.var-left-minus, term=3*x

3+3*x == 24

⇒ algebra.equations.linear.balance.con-right-minus, term=3

3*x == 21

⇒ algebra.equations.linear.balance.scale-to-one, factor=3

x == 7

13.

5*x+7 == 2*x-10

⇒ algebra.equations.linear.balance.var-left-minus, term=2*x

3*x+7 == -10

⇒ algebra.equations.linear.balance.con-right-minus, term=7

3*x == -17

⇒ algebra.equations.linear.balance.scale-to-one, factor=3

x == -17/3

14.

2*x-8 == 18-x

⇒ algebra.equations.linear.balance.var-left-plus, term=x

3*x-8 == 18

⇒ algebra.equations.linear.balance.con-right-plus, term=8

3*x == 26

⇒ algebra.equations.linear.balance.scale-to-one, factor=3

x == 26/3

15.

4*x-6 == 7*x-14

⇒ algebra.equations.linear.balance.var-right-minus, term=4*x

-6 == 3*x-14

⇒ algebra.equations.linear.balance.con-left-plus, term=14

8 == 3*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=3

8/3 == x

⇒ algebra.equations.linear.flip

x == 8/3

16.

-1-5*x == 3*x-20

⇒ algebra.equations.linear.balance.var-right-plus, term=5*x

-1 == 8*x-20

⇒ algebra.equations.linear.balance.con-left-plus, term=20

19 == 8*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=8

19/8 == x

⇒ algebra.equations.linear.flip

x == 19/8

17.

4*x-7 == -5*x-24

⇒ algebra.equations.linear.balance.var-left-plus, term=5*x

9*x-7 == -24

⇒ algebra.equations.linear.balance.con-right-plus, term=7

9*x == -17

⇒ algebra.equations.linear.balance.scale-to-one, factor=9

x == -17/9

18.

4*x-18 == 14+11*x

⇒ algebra.equations.linear.balance.var-right-minus, term=4*x

-18 == 14+7*x

⇒ algebra.equations.linear.balance.con-left-minus, term=14

-32 == 7*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=7

-32/7 == x

⇒ algebra.equations.linear.flip

x == -32/7

19.

17 == 4-10*x

⇒ algebra.equations.linear.balance.con-left-minus, term=4

13 == -10*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=-10

-13/10 == x

⇒ algebra.equations.linear.flip

x == -13/10

20.

-5*x+6 == 2-3*x

⇒ algebra.equations.linear.balance.var-right-plus, term=5*x

6 == 2+2*x

⇒ algebra.equations.linear.balance.con-left-minus, term=2

4 == 2*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=2

2 == x

⇒ algebra.equations.linear.flip

x == 2

21.

4*(x-1) == 11*x-12

⇒ algebra.equations.linear.balance.distribute

4*x-4 == 11*x-12

⇒ algebra.equations.linear.balance.var-right-minus, term=4*x

-4 == 7*x-12

⇒ algebra.equations.linear.balance.con-left-plus, term=12

8 == 7*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=7

8/7 == x

⇒ algebra.equations.linear.flip

x == 8/7

22.

4*(x-4) == 5*(2*x+1)

⇒ algebra.equations.linear.balance.distribute

4*x-16 == 10*x+5

⇒ algebra.equations.linear.balance.var-right-minus, term=4*x

-16 == 6*x+5

⇒ algebra.equations.linear.balance.con-left-minus, term=5

-21 == 6*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=6

-7/2 == x

⇒ algebra.equations.linear.flip

x == -7/2

23.

2*(5-3*x) == 6-x

⇒ algebra.equations.linear.balance.distribute

10-6*x == 6-x

⇒ algebra.equations.linear.balance.var-right-plus, term=6*x

10 == 6+5*x

⇒ algebra.equations.linear.balance.con-left-minus, term=6

4 == 5*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=5

4/5 == x

⇒ algebra.equations.linear.flip

x == 4/5

24.

4*x-(x-2) == 12+5*(x-1)

⇒ algebra.equations.linear.balance.distribute

4*x-x+2 == 12+5*x-5

⇒ algebra.equations.linear.balance.collect

3*x+2 == 7+5*x

⇒ algebra.equations.linear.balance.var-right-minus, term=3*x

2 == 7+2*x

⇒ algebra.equations.linear.balance.con-left-minus, term=7

-5 == 2*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=2

-5/2 == x

⇒ algebra.equations.linear.flip

x == -5/2

25.

-3*(x-2) == 3*(x+4)-7

⇒ algebra.equations.linear.balance.distribute

-3*x+6 == 3*x+5

⇒ algebra.equations.linear.balance.var-right-plus, term=3*x

6 == 6*x+5

⇒ algebra.equations.linear.balance.con-left-minus, term=5

1 == 6*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=6

1/6 == x

⇒ algebra.equations.linear.flip

x == 1/6

26.

3*(4*x-1)+3 == 7*x-14

⇒ algebra.equations.linear.balance.distribute

12*x == 7*x-14

⇒ algebra.equations.linear.balance.var-left-minus, term=7*x

5*x == -14

⇒ algebra.equations.linear.balance.scale-to-one, factor=5

x == -14/5

27.

4*(4*x-1)-2 == -3*x+3*(2*x-5)

⇒ algebra.equations.linear.balance.distribute

16*x-6 == -3*x+6*x-15

⇒ algebra.equations.linear.balance.collect

16*x-6 == 3*x-15

⇒ algebra.equations.linear.balance.var-left-minus, term=3*x

13*x-6 == -15

⇒ algebra.equations.linear.balance.con-right-plus, term=6

13*x == -9

⇒ algebra.equations.linear.balance.scale-to-one, factor=13

x == -9/13

28.

2*x-(3*x+5) == 10+5*(x-1)

⇒ algebra.equations.linear.balance.distribute

2*x-3*x-5 == 10+5*x-5

⇒ algebra.equations.linear.balance.collect

-x-5 == 5+5*x

⇒ algebra.equations.linear.balance.var-right-plus, term=x

-5 == 5+6*x

⇒ algebra.equations.linear.balance.con-left-minus, term=5

-10 == 6*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=6

-5/3 == x

⇒ algebra.equations.linear.flip

x == -5/3

29.

-5*(x+1) == 9*(x+4)-5

⇒ algebra.equations.linear.balance.distribute

-5*x-5 == 9*x+31

⇒ algebra.equations.linear.balance.var-right-plus, term=5*x

-5 == 14*x+31

⇒ algebra.equations.linear.balance.con-left-minus, term=31

-36 == 14*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=14

-18/7 == x

⇒ algebra.equations.linear.flip

x == -18/7

30.

18-2*(4*x+2) == 7*x-4*(4*x-2)

⇒ algebra.equations.linear.balance.distribute

18-8*x-4 == 7*x-16*x+8

⇒ algebra.equations.linear.balance.collect

14-8*x == -9*x+8

⇒ algebra.equations.linear.balance.var-left-plus, term=9*x

14+x == 8

⇒ algebra.equations.linear.balance.con-right-minus, term=14

x == -6

31.

1/2*x-4 == 2*x+2[1/2]

⇒ algebra.equations.linear.balance.remove-div, factor=2

x-8 == 4*x+5

⇒ algebra.equations.linear.balance.var-right-minus, term=x

-8 == 3*x+5

⇒ algebra.equations.linear.balance.con-left-minus, term=5

-13 == 3*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=3

-13/3 == x

⇒ algebra.equations.linear.flip

x == -13/3

32.

1/4*x+1/2 == 5/2*x+2

⇒ algebra.equations.linear.balance.remove-div, factor=4

x+2 == 10*x+8

⇒ algebra.equations.linear.balance.var-right-minus, term=x

2 == 9*x+8

⇒ algebra.equations.linear.balance.con-left-minus, term=8

-6 == 9*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=9

-2/3 == x

⇒ algebra.equations.linear.flip

x == -2/3

33.

1/4*x-3/4 == 2*x+1/2

⇒ algebra.equations.linear.balance.remove-div, factor=4

x-3 == 8*x+2

⇒ algebra.equations.linear.balance.var-right-minus, term=x

-3 == 7*x+2

⇒ algebra.equations.linear.balance.con-left-minus, term=2

-5 == 7*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=7

-5/7 == x

⇒ algebra.equations.linear.flip

x == -5/7

34.

-1/2*x+3/4 == 5/2*x+3

⇒ algebra.equations.linear.balance.remove-div, factor=4

-2*x+3 == 10*x+12

⇒ algebra.equations.linear.balance.var-right-plus, term=2*x

3 == 12*x+12

⇒ algebra.equations.linear.balance.con-left-minus, term=12

-9 == 12*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=12

-3/4 == x

⇒ algebra.equations.linear.flip

x == -3/4

35.

-1/2*x+1[1/2] == 2*x-5

⇒ algebra.equations.linear.balance.remove-div, factor=2

-x+3 == 4*x-10

⇒ algebra.equations.linear.balance.var-right-plus, term=x

3 == 5*x-10

⇒ algebra.equations.linear.balance.con-left-plus, term=10

13 == 5*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=5

13/5 == x

⇒ algebra.equations.linear.flip

x == 13/5

36.

-1/3*x+3/4 == 1/4*x+1/6

⇒ algebra.equations.linear.balance.remove-div, factor=12

-4*x+9 == 3*x+2

⇒ algebra.equations.linear.balance.var-right-plus, term=4*x

9 == 7*x+2

⇒ algebra.equations.linear.balance.con-left-minus, term=2

7 == 7*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=7

1 == x

⇒ algebra.equations.linear.flip

x == 1

37.

3/4*x-1/3 == 2/3*x-3/4

⇒ algebra.equations.linear.balance.remove-div, factor=12

9*x-4 == 8*x-9

⇒ algebra.equations.linear.balance.var-left-minus, term=8*x

x-4 == -9

⇒ algebra.equations.linear.balance.con-right-plus, term=4

x == -5

38.

2/5*x-1/4 == 1/2*x+3/4

⇒ algebra.equations.linear.balance.remove-div, factor=20

8*x-5 == 10*x+15

⇒ algebra.equations.linear.balance.var-right-minus, term=8*x

-5 == 2*x+15

⇒ algebra.equations.linear.balance.con-left-minus, term=15

-20 == 2*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=2

-10 == x

⇒ algebra.equations.linear.flip

x == -10

39.

2/3*x-2 == 1/5*x-3/5

⇒ algebra.equations.linear.balance.remove-div, factor=15

10*x-30 == 3*x-9

⇒ algebra.equations.linear.balance.var-left-minus, term=3*x

7*x-30 == -9

⇒ algebra.equations.linear.balance.con-right-plus, term=30

7*x == 21

⇒ algebra.equations.linear.balance.scale-to-one, factor=7

x == 3

40.

(-1[2/5])*x+3[1/2] == 3/5*x+9/10

⇒ algebra.equations.linear.balance.remove-div, factor=10

-14*x+35 == 6*x+9

⇒ algebra.equations.linear.balance.var-right-plus, term=14*x

35 == 20*x+9

⇒ algebra.equations.linear.balance.con-left-minus, term=9

26 == 20*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=20

13/10 == x

⇒ algebra.equations.linear.flip

x == 13/10

41.

1/4*(x-3) == 1/2*x-4

⇒ algebra.equations.linear.balance.remove-div, factor=4

x-3 == 2*x-16

⇒ algebra.equations.linear.balance.var-right-minus, term=x

-3 == x-16

⇒ algebra.equations.linear.balance.con-left-plus, term=16

13 == x

⇒ algebra.equations.linear.flip

x == 13

42.

(x+3)/2 == 5*(1/2*x+1[1/2])

⇒ algebra.equations.linear.balance.remove-div, factor=2

x+3 == 10*(1/2*x+3/2)

⇒ algebra.equations.linear.balance.distribute

x+3 == 5*x+15

⇒ algebra.equations.linear.balance.var-right-minus, term=x

3 == 4*x+15

⇒ algebra.equations.linear.balance.con-left-minus, term=15

-12 == 4*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=4

-3 == x

⇒ algebra.equations.linear.flip

x == -3

43.

1/2*(7-2/3*x) == 2+1/9*x

⇒ algebra.equations.linear.balance.remove-div, factor=18

9*(7-2/3*x) == 36+2*x

⇒ algebra.equations.linear.balance.distribute

63-6*x == 36+2*x

⇒ algebra.equations.linear.balance.var-right-plus, term=6*x

63 == 36+8*x

⇒ algebra.equations.linear.balance.con-left-minus, term=36

27 == 8*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=8

27/8 == x

⇒ algebra.equations.linear.flip

x == 27/8

44.

3/4*x-(x-1) == 3+2[1/2]*(x-1)

⇒ algebra.equations.linear.balance.distribute

3/4*x-x+1 == 3+5/2*x-5/2

⇒ algebra.equations.linear.balance.remove-div, factor=4

3*x-4*x+4 == 12+10*x-10

⇒ algebra.equations.linear.balance.collect

-x+4 == 2+10*x

⇒ algebra.equations.linear.balance.var-right-plus, term=x

4 == 2+11*x

⇒ algebra.equations.linear.balance.con-left-minus, term=2

2 == 11*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=11

2/11 == x

⇒ algebra.equations.linear.flip

x == 2/11

45.

-5/4*(x-7) == 3/4*(x+2)-4[1/2]

⇒ algebra.equations.linear.balance.remove-div, factor=4

-5*(x-7) == 3*(x+2)-18

⇒ algebra.equations.linear.balance.distribute

-5*x+35 == 3*x-12

⇒ algebra.equations.linear.balance.var-right-plus, term=5*x

35 == 8*x-12

⇒ algebra.equations.linear.balance.con-left-plus, term=12

47 == 8*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=8

47/8 == x

⇒ algebra.equations.linear.flip

x == 47/8

46.

3*(1/5*x-1)+5 == 7*x-14

⇒ algebra.equations.linear.balance.distribute

3/5*x+2 == 7*x-14

⇒ algebra.equations.linear.balance.remove-div, factor=5

3*x+10 == 35*x-70

⇒ algebra.equations.linear.balance.var-right-minus, term=3*x

10 == 32*x-70

⇒ algebra.equations.linear.balance.con-left-plus, term=70

80 == 32*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=32

5/2 == x

⇒ algebra.equations.linear.flip

x == 5/2

47.

(5*x-1)/6-2 == -4*x+(3*x-6)/2

⇒ algebra.equations.linear.balance.remove-div, factor=6

5*x-13 == -24*x+3*(3*x-6)

⇒ algebra.equations.linear.balance.distribute

5*x-13 == -24*x+9*x-18

⇒ algebra.equations.linear.balance.collect

5*x-13 == -15*x-18

⇒ algebra.equations.linear.balance.var-left-plus, term=15*x

20*x-13 == -18

⇒ algebra.equations.linear.balance.con-right-plus, term=13

20*x == -5

⇒ algebra.equations.linear.balance.scale-to-one, factor=20

x == -1/4

48.

2*x-(2*x+2)/5 == 12+(x-1)/6

⇒ algebra.equations.linear.balance.remove-div, factor=30

60*x+6*(-2*x-2) == 360+5*(x-1)

⇒ algebra.equations.linear.balance.distribute

60*x-12*x-12 == 360+5*x-5

⇒ algebra.equations.linear.balance.collect

48*x-12 == 355+5*x

⇒ algebra.equations.linear.balance.var-left-minus, term=5*x

43*x-12 == 355

⇒ algebra.equations.linear.balance.con-right-plus, term=12

43*x == 367

⇒ algebra.equations.linear.balance.scale-to-one, factor=43

x == 367/43

49.

(-3*(x+2))/6 == 9*(2/3*x+1/3)-5/3

⇒ algebra.equations.linear.balance.remove-div, factor=6

-3*(x+2) == 54*(2/3*x+1/3)-10

⇒ algebra.equations.linear.balance.distribute

-3*x-6 == 36*x+8

⇒ algebra.equations.linear.balance.var-right-plus, term=3*x

-6 == 39*x+8

⇒ algebra.equations.linear.balance.con-left-minus, term=8

-14 == 39*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=39

-14/39 == x

⇒ algebra.equations.linear.flip

x == -14/39

50.

1-(4*x+2)/3 == 3*x-(5*x-1)/4

⇒ algebra.equations.linear.balance.remove-div, factor=12

12+4*(-4*x-2) == 36*x+3*(-5*x+1)

⇒ algebra.equations.linear.balance.distribute

12-16*x-8 == 36*x-15*x+3

⇒ algebra.equations.linear.balance.collect

4-16*x == 21*x+3

⇒ algebra.equations.linear.balance.var-right-plus, term=16*x

4 == 37*x+3

⇒ algebra.equations.linear.balance.con-left-minus, term=3

1 == 37*x

⇒ algebra.equations.linear.balance.scale-to-one, factor=37

1/37 == x

⇒ algebra.equations.linear.flip

x == 1/37