Exercise algebra.equations.linear.mixed

5*x == 15

x == 3

2.

11*x-12 == 21

11*x == 33

x == 3

3.

19-3*x == -5

3*x == 24

x == 8

4.

-12+5*x == 33

5*x == 45

x == 9

5.

15-9*x == 6

9*x == 9

x == 1

6.

4*x+18 == 0

4*x == -18

x == -4[1/2]

7.

11*x-12 == -34

11*x == -22

x == -2

8.

-2*x-3 == -4

-2*x == -1

x == 1/2

9.

6*x-12 == 2

6*x == 14

x == 2[1/3]

10.

-4*x-13 == -11

-4*x == 2

x == -1/2

11.

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

4*x-2 == 14

4*x == 16

x == 4

12.

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

3+3*x == 24

3*x == 21

x == 7

13.

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

3*x+7 == -10

3*x == -17

x == -5[2/3]

14.

2*x-8 == 18-x

⇒ algebra.equations.linear.var-left, term=(-1)*x

3*x-8 == 18

3*x == 26

x == 8[2/3]

15.

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

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

-3*x-6 == -14

-3*x == -8

x == 2[2/3]

16.

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

-1-8*x == -20

8*x == 19

x == 2[3/8]

17.

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

⇒ algebra.equations.linear.var-left, term=(-5)*x

9*x-7 == -24

9*x == -17

x == -1[8/9]

18.

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

⇒ algebra.equations.linear.var-left, term=11*x

-7*x-18 == 14

-7*x == 32

x == -4[4/7]

19.

17 == 4-10*x

⇒ algebra.equations.linear.flip

4-10*x == 17

10*x == -13

x == -1[3/10]

20.

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

⇒ algebra.equations.linear.var-left, term=(-3)*x

-2*x+6 == 2

-2*x == -4

x == 2

21.

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

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

⇒ algebra.equations.linear.var-left, term=11*x

-7*x-4 == -12

-7*x == -8

x == 1[1/7]

22.

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

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

⇒ algebra.equations.linear.var-left, term=10*x

-6*x-16 == 5

-6*x == 21

x == -3[1/2]

23.

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

10-6*x == 6-x

⇒ algebra.equations.linear.var-left, term=(-1)*x

10-5*x == 6

5*x == 4

x == 4/5

24.

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

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

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

-2*x+2 == 7

-2*x == 5

x == -2[1/2]

25.

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

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

-6*x+6 == 5

-6*x == -1

x == 1/6

26.

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

12*x == 7*x-14

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

5*x == -14

x == -2[4/5]

27.

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

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

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

13*x-6 == -15

13*x == -9

x == -9/13

28.

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

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

-x-5 == 5+5*x

-6*x-5 == 5

-6*x == 10

x == -1[2/3]

29.

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

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

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

-14*x-5 == 31

-14*x == 36

x == -2[4/7]

30.

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

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

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

⇒ algebra.equations.linear.var-left, term=(-9)*x

14+x == 8

x == -6

31.

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

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

x-8 == 4*x+5

⇒ algebra.equations.linear.var-left, term=4*x

-3*x-8 == 5

-3*x == 13

x == -4[1/3]

32.

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

x+2 == 10*x+8

⇒ algebra.equations.linear.var-left, term=10*x

-9*x+2 == 8

-9*x == 6

x == -2/3

33.

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

x-3 == 8*x+2

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

-7*x-3 == 2

-7*x == 5

x == -5/7

34.

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

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

⇒ algebra.equations.linear.var-left, term=10*x

-12*x+3 == 12

-12*x == 9

x == -3/4

35.

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

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

-x+3 == 4*x-10

⇒ algebra.equations.linear.var-left, term=4*x

-5*x+3 == -10

-5*x == -13

x == 2[3/5]

36.

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

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

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

-7*x+9 == 2

-7*x == -7

x == 1

37.

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

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

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

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

x-4 == -9

x == -5

38.

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

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

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

⇒ algebra.equations.linear.var-left, term=10*x

-2*x-5 == 15

-2*x == 20

x == -10

39.

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

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

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

7*x-30 == -9

7*x == 21

x == 3

40.

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

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

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

⇒ algebra.equations.linear.var-left, term=6*x

-20*x+35 == 9

-20*x == -26

x == 1[3/10]

41.

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

x-3 == 2*x-16

-x-3 == -16

-x == -13

⇒ algebra.equations.coverup.negate

x == 13

42.

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

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

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

x+3 == 5*x+15

-4*x+3 == 15

-4*x == 12

x == -3

43.

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

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

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

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

63-8*x == 36

8*x == 27

x == 3[3/8]

44.

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

-x+4 == 12+10*(x-1)

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

-x+4 == 2+10*x

⇒ algebra.equations.linear.var-left, term=10*x

-11*x+4 == 2

-11*x == -2

x == 2/11

45.

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

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

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

-8*x+35 == -12

-8*x == -47

x == 5[7/8]

46.

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

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

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

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

⇒ algebra.equations.linear.var-left, term=35*x

-32*x+10 == -70

-32*x == -80

x == 2[1/2]

47.

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

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

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

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

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

⇒ algebra.equations.linear.var-left, term=(-15)*x

20*x-13 == -18

20*x == -5

x == -1/4

48.

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

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

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

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

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

43*x-12 == 355

43*x == 367

x == 8[23/43]

49.

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

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

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

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

⇒ algebra.equations.linear.var-left, term=36*x

-39*x-6 == 8

-39*x == 14

x == -14/39

50.

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

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

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

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

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

⇒ algebra.equations.linear.var-left, term=21*x

4-37*x == 3

37*x == 1