-711k+2<23

Combine k and 711.

-k⋅711+2<23

Move 7 to the left of k.

-7k11+2<23

-7k11+2<23

Subtract 2 from both sides of the inequality.

-7k11<23-2

To write -2 as a fraction with a common denominator, multiply by 33.

-7k11<23-2⋅33

Combine -2 and 33.

-7k11<23+-2⋅33

Combine the numerators over the common denominator.

-7k11<2-2⋅33

Simplify the numerator.

Multiply -2 by 3.

-7k11<2-63

Subtract 6 from 2.

-7k11<-43

-7k11<-43

Move the negative in front of the fraction.

-7k11<-43

-7k11<-43

Multiply each term in -7k11<-43 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-7k11⋅-1>-43⋅-1

Multiply -7k11⋅-1.

Multiply -1 by -1.

17k11>-43⋅-1

Multiply 7k11 by 1.

7k11>-43⋅-1

7k11>-43⋅-1

Multiply -43⋅-1.

Multiply -1 by -1.

7k11>1(43)

Multiply 43 by 1.

7k11>43

7k11>43

7k11>43

Multiply both sides of the equation by 11.

7k>43⋅(11)

Combine 43 and 11.

7k>4⋅113

Multiply 4 by 11.

7k>443

7k>443

Divide each term in 7k>443 by 7.

7k7>443⋅17

Cancel the common factor of 7.

Cancel the common factor.

7k7>443⋅17

Divide k by 1.

k>443⋅17

k>443⋅17

Multiply 443⋅17.

Multiply 443 and 17.

k>443⋅7

Multiply 3 by 7.

k>4421

k>4421

k>4421

The result can be shown in multiple forms.

Inequality Form:

k>4421

Interval Notation:

(4421,∞)

Solve for k -7/11k+2<2/3