Exercise algebra.equations.linear.mixed
Description
solve a linear equation with mixed fractions
Derivations
1.
2.
11*x-12 == 21
⇒ algebra.equations.coverup.onevar.minus-left11*x == 33
⇒ algebra.equations.coverup.timesx == 3
3.
19-3*x == -5
⇒ algebra.equations.coverup.onevar.minus-right3*x == 24
⇒ algebra.equations.coverup.timesx == 8
4.
-12+5*x == 33
⇒ algebra.equations.coverup.onevar.plus5*x == 45
⇒ algebra.equations.coverup.timesx == 9
5.
15-9*x == 6
⇒ algebra.equations.coverup.onevar.minus-right9*x == 9
⇒ algebra.equations.coverup.timesx == 1
6.
4*x+18 == 0
⇒ algebra.equations.coverup.onevar.plus4*x == -18
⇒ algebra.equations.coverup.timesx == -4[1/2]
7.
11*x-12 == -34
⇒ algebra.equations.coverup.onevar.minus-left11*x == -22
⇒ algebra.equations.coverup.timesx == -2
8.
-2*x-3 == -4
⇒ algebra.equations.coverup.onevar.minus-left-2*x == -1
⇒ algebra.equations.coverup.timesx == 1/2
9.
6*x-12 == 2
⇒ algebra.equations.coverup.onevar.minus-left6*x == 14
⇒ algebra.equations.coverup.timesx == 2[1/3]
10.
-4*x-13 == -11
⇒ algebra.equations.coverup.onevar.minus-left-4*x == 2
⇒ algebra.equations.coverup.timesx == -1/2
11.
6*x-2 == 2*x+14
⇒ algebra.equations.linear.var-left, term=2*x4*x-2 == 14
⇒ algebra.equations.coverup.onevar.minus-left4*x == 16
⇒ algebra.equations.coverup.timesx == 4
12.
3+6*x == 3*x+24
⇒ algebra.equations.linear.var-left, term=3*x3+3*x == 24
⇒ algebra.equations.coverup.onevar.plus3*x == 21
⇒ algebra.equations.coverup.timesx == 7
13.
5*x+7 == 2*x-10
⇒ algebra.equations.linear.var-left, term=2*x3*x+7 == -10
⇒ algebra.equations.coverup.onevar.plus3*x == -17
⇒ algebra.equations.coverup.timesx == -5[2/3]
14.
2*x-8 == 18-x
⇒ algebra.equations.linear.var-left, term=(-1)*x3*x-8 == 18
⇒ algebra.equations.coverup.onevar.minus-left3*x == 26
⇒ algebra.equations.coverup.timesx == 8[2/3]
15.
4*x-6 == 7*x-14
⇒ algebra.equations.linear.var-left, term=7*x-3*x-6 == -14
⇒ algebra.equations.coverup.onevar.minus-left-3*x == -8
⇒ algebra.equations.coverup.timesx == 2[2/3]
16.
-1-5*x == 3*x-20
⇒ algebra.equations.linear.var-left, term=3*x-1-8*x == -20
⇒ algebra.equations.coverup.onevar.minus-right8*x == 19
⇒ algebra.equations.coverup.timesx == 2[3/8]
17.
4*x-7 == -5*x-24
⇒ algebra.equations.linear.var-left, term=(-5)*x9*x-7 == -24
⇒ algebra.equations.coverup.onevar.minus-left9*x == -17
⇒ algebra.equations.coverup.timesx == -1[8/9]
18.
4*x-18 == 14+11*x
⇒ algebra.equations.linear.var-left, term=11*x-7*x-18 == 14
⇒ algebra.equations.coverup.onevar.minus-left-7*x == 32
⇒ algebra.equations.coverup.timesx == -4[4/7]
19.
17 == 4-10*x
⇒ algebra.equations.linear.flip4-10*x == 17
⇒ algebra.equations.coverup.onevar.minus-right10*x == -13
⇒ algebra.equations.coverup.timesx == -1[3/10]
20.
-5*x+6 == 2-3*x
⇒ algebra.equations.linear.var-left, term=(-3)*x-2*x+6 == 2
⇒ algebra.equations.coverup.onevar.plus-2*x == -4
⇒ algebra.equations.coverup.timesx == 2
21.
4*(x-1) == 11*x-12
⇒ algebra.equations.linear.distr-times4*x-4 == 11*x-12
⇒ algebra.equations.linear.var-left, term=11*x-7*x-4 == -12
⇒ algebra.equations.coverup.onevar.minus-left-7*x == -8
⇒ algebra.equations.coverup.timesx == 1[1/7]
22.
4*(x-4) == 5*(2*x+1)
⇒ algebra.equations.linear.distr-times4*x-16 == 10*x+5
⇒ algebra.equations.linear.var-left, term=10*x-6*x-16 == 5
⇒ algebra.equations.coverup.onevar.minus-left-6*x == 21
⇒ algebra.equations.coverup.timesx == -3[1/2]
23.
2*(5-3*x) == 6-x
⇒ algebra.equations.linear.distr-times10-6*x == 6-x
⇒ algebra.equations.linear.var-left, term=(-1)*x10-5*x == 6
⇒ algebra.equations.coverup.onevar.minus-right5*x == 4
⇒ algebra.equations.coverup.timesx == 4/5
24.
4*x-(x-2) == 12+5*(x-1)
⇒ algebra.equations.linear.distr-times4*x-x+2 == 12+5*x-5
⇒ algebra.equations.linear.merge3*x+2 == 7+5*x
⇒ algebra.equations.linear.var-left, term=5*x-2*x+2 == 7
⇒ algebra.equations.coverup.onevar.plus-2*x == 5
⇒ algebra.equations.coverup.timesx == -2[1/2]
25.
-3*(x-2) == 3*(x+4)-7
⇒ algebra.equations.linear.distr-times-3*x+6 == 3*x+5
⇒ algebra.equations.linear.var-left, term=3*x-6*x+6 == 5
⇒ algebra.equations.coverup.onevar.plus-6*x == -1
⇒ algebra.equations.coverup.timesx == 1/6
26.
3*(4*x-1)+3 == 7*x-14
⇒ algebra.equations.linear.distr-times12*x == 7*x-14
⇒ algebra.equations.linear.var-left, term=7*x5*x == -14
⇒ algebra.equations.coverup.timesx == -2[4/5]
27.
4*(4*x-1)-2 == -3*x+3*(2*x-5)
⇒ algebra.equations.linear.distr-times16*x-6 == -3*x+6*x-15
⇒ algebra.equations.linear.merge16*x-6 == 3*x-15
⇒ algebra.equations.linear.var-left, term=3*x13*x-6 == -15
⇒ algebra.equations.coverup.onevar.minus-left13*x == -9
⇒ algebra.equations.coverup.timesx == -9/13
28.
2*x-(3*x+5) == 10+5*(x-1)
⇒ algebra.equations.linear.distr-times2*x-3*x-5 == 10+5*x-5
⇒ algebra.equations.linear.merge-x-5 == 5+5*x
⇒ algebra.equations.linear.var-left, term=5*x-6*x-5 == 5
⇒ algebra.equations.coverup.onevar.minus-left-6*x == 10
⇒ algebra.equations.coverup.timesx == -1[2/3]
29.
-5*(x+1) == 9*(x+4)-5
⇒ algebra.equations.linear.distr-times-5*x-5 == 9*x+31
⇒ algebra.equations.linear.var-left, term=9*x-14*x-5 == 31
⇒ algebra.equations.coverup.onevar.minus-left-14*x == 36
⇒ algebra.equations.coverup.timesx == -2[4/7]
30.
18-2*(4*x+2) == 7*x-4*(4*x-2)
⇒ algebra.equations.linear.distr-times18-8*x-4 == 7*x-16*x+8
⇒ algebra.equations.linear.merge14-8*x == -9*x+8
⇒ algebra.equations.linear.var-left, term=(-9)*x14+x == 8
⇒ algebra.equations.coverup.onevar.plusx == -6
31.
1/2*x-4 == 2*x+2[1/2]
⇒ algebra.equations.linear.remove-div, factor=2x-8 == 4*x+5
⇒ algebra.equations.linear.var-left, term=4*x-3*x-8 == 5
⇒ algebra.equations.coverup.onevar.minus-left-3*x == 13
⇒ algebra.equations.coverup.timesx == -4[1/3]
32.
1/4*x+1/2 == 5/2*x+2
⇒ algebra.equations.linear.remove-div, factor=4x+2 == 10*x+8
⇒ algebra.equations.linear.var-left, term=10*x-9*x+2 == 8
⇒ algebra.equations.coverup.onevar.plus-9*x == 6
⇒ algebra.equations.coverup.timesx == -2/3
33.
1/4*x-3/4 == 2*x+1/2
⇒ algebra.equations.linear.remove-div, factor=4x-3 == 8*x+2
⇒ algebra.equations.linear.var-left, term=8*x-7*x-3 == 2
⇒ algebra.equations.coverup.onevar.minus-left-7*x == 5
⇒ algebra.equations.coverup.timesx == -5/7
34.
-1/2*x+3/4 == 5/2*x+3
⇒ algebra.equations.linear.remove-div, factor=4-2*x+3 == 10*x+12
⇒ algebra.equations.linear.var-left, term=10*x-12*x+3 == 12
⇒ algebra.equations.coverup.onevar.plus-12*x == 9
⇒ algebra.equations.coverup.timesx == -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
⇒ algebra.equations.coverup.onevar.plus-5*x == -13
⇒ algebra.equations.coverup.timesx == 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
⇒ algebra.equations.linear.var-left, term=3*x-7*x+9 == 2
⇒ algebra.equations.coverup.onevar.plus-7*x == -7
⇒ algebra.equations.coverup.timesx == 1
37.
3/4*x-1/3 == 2/3*x-3/4
⇒ algebra.equations.linear.remove-div, factor=129*x-4 == 8*x-9
⇒ algebra.equations.linear.var-left, term=8*xx-4 == -9
⇒ algebra.equations.coverup.onevar.minus-leftx == -5
38.
2/5*x-1/4 == 1/2*x+3/4
⇒ algebra.equations.linear.remove-div, factor=208*x-5 == 10*x+15
⇒ algebra.equations.linear.var-left, term=10*x-2*x-5 == 15
⇒ algebra.equations.coverup.onevar.minus-left-2*x == 20
⇒ algebra.equations.coverup.timesx == -10
39.
2/3*x-2 == 1/5*x-3/5
⇒ algebra.equations.linear.remove-div, factor=1510*x-30 == 3*x-9
⇒ algebra.equations.linear.var-left, term=3*x7*x-30 == -9
⇒ algebra.equations.coverup.onevar.minus-left7*x == 21
⇒ algebra.equations.coverup.timesx == 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
⇒ algebra.equations.coverup.onevar.plus-20*x == -26
⇒ algebra.equations.coverup.timesx == 1[3/10]
41.
1/4*(x-3) == 1/2*x-4
⇒ algebra.equations.linear.remove-div, factor=4x-3 == 2*x-16
⇒ algebra.equations.linear.var-left, term=2*x-x-3 == -16
⇒ algebra.equations.coverup.onevar.minus-left-x == -13
⇒ algebra.equations.coverup.negatex == 13
42.
(x+3)/2 == 5*(1/2*x+1[1/2])
⇒ algebra.equations.linear.remove-div, factor=2x+3 == 10*(1/2*x+1[1/2])
⇒ algebra.equations.linear.distr-timesx+3 == 5*x+15
⇒ algebra.equations.linear.var-left, term=5*x-4*x+3 == 15
⇒ algebra.equations.coverup.onevar.plus-4*x == 12
⇒ algebra.equations.coverup.timesx == -3
43.
1/2*(7-2/3*x) == 2+1/9*x
⇒ algebra.equations.linear.remove-div, factor=189*(7-2/3*x) == 36+2*x
⇒ algebra.equations.linear.distr-times63-6*x == 36+2*x
⇒ algebra.equations.linear.var-left, term=2*x63-8*x == 36
⇒ algebra.equations.coverup.onevar.minus-right8*x == 27
⇒ algebra.equations.coverup.timesx == 3[3/8]
44.
3/4*x-(x-1) == 3+2[1/2]*(x-1)
⇒ algebra.equations.linear.remove-div, factor=4-x+4 == 12+10*(x-1)
⇒ algebra.equations.linear.distr-times-x+4 == 12+10*x-10
⇒ algebra.equations.linear.merge-x+4 == 2+10*x
⇒ algebra.equations.linear.var-left, term=10*x-11*x+4 == 2
⇒ algebra.equations.coverup.onevar.plus-11*x == -2
⇒ algebra.equations.coverup.timesx == 2/11
45.
-5/4*(x-7) == 3/4*(x+2)-4[1/2]
⇒ algebra.equations.linear.remove-div, factor=4-5*(x-7) == 3*(x+2)-18
⇒ algebra.equations.linear.distr-times-5*x+35 == 3*x-12
⇒ algebra.equations.linear.var-left, term=3*x-8*x+35 == -12
⇒ algebra.equations.coverup.onevar.plus-8*x == -47
⇒ algebra.equations.coverup.timesx == 5[7/8]
46.
3*(1/5*x-1)+5 == 7*x-14
⇒ algebra.equations.linear.distr-times3/5*x+2 == 7*x-14
⇒ algebra.equations.linear.remove-div, factor=53*x+10 == 35*x-70
⇒ algebra.equations.linear.var-left, term=35*x-32*x+10 == -70
⇒ algebra.equations.coverup.onevar.plus-32*x == -80
⇒ algebra.equations.coverup.timesx == 2[1/2]
47.
(5*x-1)/6-2 == -4*x+(3*x-6)/2
⇒ algebra.equations.linear.remove-div, factor=65*x-13 == -24*x+3*(3*x-6)
⇒ algebra.equations.linear.distr-times5*x-13 == -24*x+9*x-18
⇒ algebra.equations.linear.merge5*x-13 == -15*x-18
⇒ algebra.equations.linear.var-left, term=(-15)*x20*x-13 == -18
⇒ algebra.equations.coverup.onevar.minus-left20*x == -5
⇒ algebra.equations.coverup.timesx == -1/4
48.
2*x-(2*x+2)/5 == 12+(x-1)/6
⇒ algebra.equations.linear.remove-div, factor=3060*x-6*(2*x+2) == 360+5*(x-1)
⇒ algebra.equations.linear.distr-times60*x-12*x-12 == 360+5*x-5
⇒ algebra.equations.linear.merge48*x-12 == 355+5*x
⇒ algebra.equations.linear.var-left, term=5*x43*x-12 == 355
⇒ algebra.equations.coverup.onevar.minus-left43*x == 367
⇒ algebra.equations.coverup.timesx == 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
⇒ algebra.equations.linear.distr-times-3*x-6 == 36*x+8
⇒ algebra.equations.linear.var-left, term=36*x-39*x-6 == 8
⇒ algebra.equations.coverup.onevar.minus-left-39*x == 14
⇒ algebra.equations.coverup.timesx == -14/39
50.
1-(4*x+2)/3 == 3*x-(5*x-1)/4
⇒ algebra.equations.linear.remove-div, factor=1212-4*(4*x+2) == 36*x-3*(5*x-1)
⇒ algebra.equations.linear.distr-times12-16*x-8 == 36*x-15*x+3
⇒ algebra.equations.linear.merge4-16*x == 21*x+3
⇒ algebra.equations.linear.var-left, term=21*x4-37*x == 3
⇒ algebra.equations.coverup.onevar.minus-right37*x == 1
⇒ algebra.equations.coverup.timesx == 1/37