Exercise algebra.inequalities.linear

Description
solve a linear inequation

Derivations

1.

7*x-12 < 5*x+3

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

2*x-12 < 3

⇒ algebra.equations.coverup.onevar.minus-left

2*x < 15

⇒ algebra.equations.coverup.times-positive

x < 15/2

2.

4*(x-3) > 3*(x-4)

⇒ algebra.equations.linear.distr-times

4*x-12 > 3*x-12

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

x-12 > -12

⇒ algebra.equations.coverup.onevar.minus-left

x > 0

3.

6*(a+1) < 3*(a-2)+4

⇒ algebra.equations.linear.distr-times

6*a+6 < 3*a-2

⇒ algebra.equations.linear.var-left, term=3*a

3*a+6 < -2

⇒ algebra.equations.coverup.onevar.plus

3*a < -8

⇒ algebra.equations.coverup.times-positive

a < -8/3

4.

5-2*(a-3) > 5*(3-a)

⇒ algebra.equations.linear.distr-times

5-2*a+6 > 15-5*a

⇒ algebra.equations.linear.merge

11-2*a > 15-5*a

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

11+3*a > 15

⇒ algebra.equations.coverup.onevar.plus

3*a > 4

⇒ algebra.equations.coverup.times-positive

a > 4/3

5.

4*x+5 < 5*x-3

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

-x+5 < -3

⇒ algebra.equations.coverup.onevar.plus

-x < -8

⇒ algebra.inequalities.flip-sign

x > 8

6.

1/3*x+10 > 1/2*x

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

2*x+60 > 3*x

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

-x+60 > 0

⇒ algebra.equations.coverup.onevar.plus

-x > -60

⇒ algebra.inequalities.flip-sign

x < 60

7.

3*x+1 < 7*x+5

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

-4*x+1 < 5

⇒ algebra.equations.coverup.onevar.plus

-4*x < 4

⇒ algebra.inequalities.flip-sign

4*x > -4

⇒ algebra.equations.coverup.times-positive

x > -1

8.

x+6 > 2-3/4*x

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

4*x+24 > 8-3*x

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

7*x+24 > 8

⇒ algebra.equations.coverup.onevar.plus

7*x > -16

⇒ algebra.equations.coverup.times-positive

x > -16/7

9.

5*(x-1) < 7*x-1

⇒ algebra.equations.linear.distr-times

5*x-5 < 7*x-1

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

-2*x-5 < -1

⇒ algebra.equations.coverup.onevar.minus-left

-2*x < 4

⇒ algebra.inequalities.flip-sign

2*x > -4

⇒ algebra.equations.coverup.times-positive

x > -2

10.

-3*(4*x-1) > 2-(x-1)

⇒ algebra.equations.linear.distr-times

-12*x+3 > 2-x+1

⇒ algebra.equations.linear.merge

-12*x+3 > 3-x

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

-11*x+3 > 3

⇒ algebra.equations.coverup.onevar.plus

-11*x > 0

⇒ algebra.inequalities.flip-sign

11*x < 0

⇒ algebra.equations.coverup.times-positive

x < 0

11.

2*(3*x-1) < 5-(2-9*x)

⇒ algebra.equations.linear.distr-times

6*x-2 < 3+9*x

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

-3*x-2 < 3

⇒ algebra.equations.coverup.onevar.minus-left

-3*x < 5

⇒ algebra.inequalities.flip-sign

3*x > -5

⇒ algebra.equations.coverup.times-positive

x > -5/3

12.

2*(x-1)-3*(x-2) > 6

⇒ algebra.equations.linear.distr-times

2*x-2-3*x+6 > 6

⇒ algebra.equations.linear.merge

-x+4 > 6

⇒ algebra.equations.coverup.onevar.plus

-x > 2

⇒ algebra.inequalities.flip-sign

x < -2

13.

(x-12)/(-2) > (x+3)/3

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

-3*(x-12) > 2*(x+3)

⇒ algebra.equations.linear.distr-times

-3*x+36 > 2*x+6

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

-5*x+36 > 6

⇒ algebra.equations.coverup.onevar.plus

-5*x > -30

⇒ algebra.inequalities.flip-sign

5*x < 30

⇒ algebra.equations.coverup.times-positive

x < 6