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

-711k+2<23
Simplify each term.
Combine k and 711.
-k⋅711+2<23
Move 7 to the left of k.
-7k11+2<23
-7k11+2<23
Move all terms not containing k to the right side of the inequality.
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
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)
Multiply 43(11).
Combine 43 and 11.
7k>4⋅113
Multiply 4 by 11.
7k>443
7k>443
Divide each term by 7 and simplify.
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