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Exercise

Exercise algebra.equations.coverup

Description
solve an equation by covering up

Derivations

1.

x-2 == 2
⇒ algebra.equations.coverup.minus-left
x == 4

2.

-4*x == -28
⇒ algebra.equations.coverup.negate
4*x == 28
⇒ algebra.equations.coverup.times
x == 7

3.

-8*x == 72
⇒ algebra.equations.coverup.negate
8*x == -72
⇒ algebra.equations.coverup.times
x == -9

4.

x+4 == 9
⇒ algebra.equations.coverup.plus
x == 5

5.

4+x == 2
⇒ algebra.equations.coverup.plus
x == -2

6.

-10-x == -7
⇒ algebra.equations.coverup.minus-right
x == -3

7.

x/(-8) == -3
⇒ algebra.equations.coverup.numerator
x == 24

8.

11-x == 14
⇒ algebra.equations.coverup.minus-right
x == -3

9.

-5-3*x == -23
⇒ algebra.equations.coverup.minus-right
3*x == 18
⇒ algebra.equations.coverup.times
x == 6

10.

21/x-4 == 3
⇒ algebra.equations.coverup.minus-left
21/x == 7
⇒ algebra.equations.coverup.denominator
x == 3

11.

-3*(x+3) == -27
⇒ algebra.equations.coverup.negate
3*(x+3) == 27
⇒ algebra.equations.coverup.times
x+3 == 9
⇒ algebra.equations.coverup.plus
x == 6

12.

2-5*x == 47
⇒ algebra.equations.coverup.minus-right
5*x == -45
⇒ algebra.equations.coverup.times
x == -9

13.

18/(7-x) == 6
⇒ algebra.equations.coverup.denominator
7-x == 3
⇒ algebra.equations.coverup.minus-right
x == 4

14.

-77/x+4 == -7
⇒ algebra.equations.coverup.plus
-77/x == -11
⇒ algebra.equations.coverup.denominator
x == 7

15.

-7-x/(-5) == -15
⇒ algebra.equations.coverup.minus-right
-x/5 == 8
⇒ algebra.equations.coverup.negate
x/5 == -8
⇒ algebra.equations.coverup.numerator
x == -40

16.

-18/(-3+x) == 3
⇒ algebra.equations.coverup.denominator
-3+x == -6
⇒ algebra.equations.coverup.plus
x == -3

17.

-5*(5-(3-x)) == -20
⇒ algebra.equations.coverup.negate
5*(2+x) == 20
⇒ algebra.equations.coverup.times
2+x == 4
⇒ algebra.equations.coverup.plus
x == 2

18.

(-20-x)/(-5)-2 == 3
⇒ algebra.equations.coverup.minus-left
-(-20-x)/5 == 5
⇒ algebra.equations.coverup.negate
(-20-x)/5 == -5
⇒ algebra.equations.coverup.numerator
-20-x == -25
⇒ algebra.equations.coverup.minus-right
x == 5

19.

4-(x-14)/(-3) == 1
⇒ algebra.equations.coverup.minus-right
-(x-14)/3 == 3
⇒ algebra.equations.coverup.negate
(x-14)/3 == -3
⇒ algebra.equations.coverup.numerator
x-14 == -9
⇒ algebra.equations.coverup.minus-left
x == 5

20.

3*x-3-7 == 8
⇒ algebra.equations.coverup.minus-left
3*x-3 == 15
⇒ algebra.equations.coverup.minus-left
3*x == 18
⇒ algebra.equations.coverup.times
x == 6

21.

-42/(-2*x+2) == 7
⇒ algebra.equations.coverup.denominator
-2*x+2 == -6
⇒ algebra.equations.coverup.plus
-2*x == -8
⇒ algebra.equations.coverup.negate
2*x == 8
⇒ algebra.equations.coverup.times
x == 4

22.

3*(4+x+2) == 12
⇒ algebra.equations.coverup.times
4+x+2 == 4
⇒ algebra.equations.coverup.plus
4+x == 2
⇒ algebra.equations.coverup.plus
x == -2

23.

-6-(-54/(-3*x)) == -12
⇒ algebra.equations.coverup.minus-right
54/(3*x) == 6
⇒ algebra.equations.coverup.denominator
3*x == 9
⇒ algebra.equations.coverup.times
x == 3

24.

14-(x-3)/4 == 3
⇒ algebra.equations.coverup.minus-right
(x-3)/4 == 11
⇒ algebra.equations.coverup.numerator
x-3 == 44
⇒ algebra.equations.coverup.minus-left
x == 47

25.

38-7*x == 3
⇒ algebra.equations.coverup.minus-right
7*x == 35
⇒ algebra.equations.coverup.times
x == 5

26.

sqrt (125/x) == 5
⇒ algebra.equations.coverup.sqrt
125/x == 25
⇒ algebra.equations.coverup.denominator
x == 5

27.

4*(12-x)+7 == 35
⇒ algebra.equations.coverup.plus
4*(12-x) == 28
⇒ algebra.equations.coverup.times
12-x == 7
⇒ algebra.equations.coverup.minus-right
x == 5

28.

5*x^2 == 80
⇒ algebra.equations.coverup.times
x^2 == 16
⇒ algebra.equations.coverup.power
x == 4 or x == -4

29.

5*(5-x) == 35
⇒ algebra.equations.coverup.times
5-x == 7
⇒ algebra.equations.coverup.minus-right
x == -2

30.

32/sqrt x == 8
⇒ algebra.equations.coverup.denominator
sqrt x == 4
⇒ algebra.equations.coverup.sqrt
x == 16

31.

21/x-8 == -1
⇒ algebra.equations.coverup.minus-left
21/x == 7
⇒ algebra.equations.coverup.denominator
x == 3

32.

180/x^2 == 5
⇒ algebra.equations.coverup.denominator
x^2 == 36
⇒ algebra.equations.coverup.power
x == 6 or x == -6

33.

3*(x-8)^2 == 12
⇒ algebra.equations.coverup.times
(x-8)^2 == 4
⇒ algebra.equations.coverup.power
x-8 == 2 or x-8 == -2
⇒ algebra.equations.coverup.minus-left
x == 10 or x-8 == -2
⇒ algebra.equations.coverup.minus-left
x == 10 or x == 6

34.

(8-x)/3+7 == 9
⇒ algebra.equations.coverup.plus
(8-x)/3 == 2
⇒ algebra.equations.coverup.numerator
8-x == 6
⇒ algebra.equations.coverup.minus-right
x == 2

35.

sqrt (x+9)/2 == 3
⇒ algebra.equations.coverup.numerator
sqrt (x+9) == 6
⇒ algebra.equations.coverup.sqrt
x+9 == 36
⇒ algebra.equations.coverup.plus
x == 27

36.

(4*x-18)^2 == 4
⇒ algebra.equations.coverup.power
4*x-18 == 2 or 4*x-18 == -2
⇒ algebra.equations.coverup.minus-left
4*x == 20 or 4*x-18 == -2
⇒ algebra.equations.coverup.minus-left
4*x == 20 or 4*x == 16
⇒ algebra.equations.coverup.times
x == 5 or 4*x == 16
⇒ algebra.equations.coverup.times
x == 5 or x == 4

37.

3*(13-2*x)^2-20 == 55
⇒ algebra.equations.coverup.minus-left
3*(13-2*x)^2 == 75
⇒ algebra.equations.coverup.times
(13-2*x)^2 == 25
⇒ algebra.equations.coverup.power
13-2*x == 5 or 13-2*x == -5
⇒ algebra.equations.coverup.minus-right
2*x == 8 or 13-2*x == -5
⇒ algebra.equations.coverup.minus-right
2*x == 8 or 2*x == 18
⇒ algebra.equations.coverup.times
x == 4 or 2*x == 18
⇒ algebra.equations.coverup.times
x == 4 or x == 9

38.

5*(x/3-8)^2 == 20
⇒ algebra.equations.coverup.times
(x/3-8)^2 == 4
⇒ algebra.equations.coverup.power
x/3-8 == 2 or x/3-8 == -2
⇒ algebra.equations.coverup.minus-left
x/3 == 10 or x/3-8 == -2
⇒ algebra.equations.coverup.minus-left
x/3 == 10 or x/3 == 6
⇒ algebra.equations.coverup.numerator
x == 30 or x/3 == 6
⇒ algebra.equations.coverup.numerator
x == 30 or x == 18

39.

(6/sqrt (x-7))^3 == 8
⇒ algebra.equations.coverup.power
6/sqrt (x-7) == 2
⇒ algebra.equations.coverup.denominator
sqrt (x-7) == 3
⇒ algebra.equations.coverup.sqrt
x-7 == 9
⇒ algebra.equations.coverup.minus-left
x == 16

40.

8-15/sqrt (31-x) == 5
⇒ algebra.equations.coverup.minus-right
15/sqrt (31-x) == 3
⇒ algebra.equations.coverup.denominator
sqrt (31-x) == 5
⇒ algebra.equations.coverup.sqrt
31-x == 25
⇒ algebra.equations.coverup.minus-right
x == 6

41.

sqrt (4*(x^2-21)) == 4
⇒ algebra.equations.coverup.sqrt
4*(x^2-21) == 16
⇒ algebra.equations.coverup.times
x^2-21 == 4
⇒ algebra.equations.coverup.minus-left
x^2 == 25
⇒ algebra.equations.coverup.power
x == 5 or x == -5

42.

3+44/sqrt (87+x) == 7
⇒ algebra.equations.coverup.plus
44/sqrt (87+x) == 4
⇒ algebra.equations.coverup.denominator
sqrt (87+x) == 11
⇒ algebra.equations.coverup.sqrt
87+x == 121
⇒ algebra.equations.coverup.plus
x == 34

43.

13-56/(21+70/(3+x)) == 12
⇒ algebra.equations.coverup.minus-right
56/(21+70/(3+x)) == 1
⇒ algebra.equations.coverup.denominator
21+70/(3+x) == 56
⇒ algebra.equations.coverup.plus
70/(3+x) == 35
⇒ algebra.equations.coverup.denominator
3+x == 2
⇒ algebra.equations.coverup.plus
x == -1

44.

12/(2+24/(8+28/(2+9/x))) == 3
⇒ algebra.equations.coverup.denominator
2+24/(8+28/(2+9/x)) == 4
⇒ algebra.equations.coverup.plus
24/(8+28/(2+9/x)) == 2
⇒ algebra.equations.coverup.denominator
8+28/(2+9/x) == 12
⇒ algebra.equations.coverup.plus
28/(2+9/x) == 4
⇒ algebra.equations.coverup.denominator
2+9/x == 7
⇒ algebra.equations.coverup.plus
9/x == 5
⇒ algebra.equations.coverup.denominator
x == 9/5
version 1.2.1.1 (revision 7140, Tue, 04 Nov 2014)