4(k+1)-8(k-2)<3(2k+2)-2

Simplify each term.

Apply the distributive property.

4k+4⋅1-8(k-2)<3(2k+2)-2

Multiply 4 by 1.

4k+4-8(k-2)<3(2k+2)-2

Apply the distributive property.

4k+4-8k-8⋅-2<3(2k+2)-2

Multiply -8 by -2.

4k+4-8k+16<3(2k+2)-2

4k+4-8k+16<3(2k+2)-2

Simplify by adding terms.

Subtract 8k from 4k.

-4k+4+16<3(2k+2)-2

Add 4 and 16.

-4k+20<3(2k+2)-2

-4k+20<3(2k+2)-2

-4k+20<3(2k+2)-2

Simplify each term.

Apply the distributive property.

-4k+20<3(2k)+3⋅2-2

Multiply 2 by 3.

-4k+20<6k+3⋅2-2

Multiply 3 by 2.

-4k+20<6k+6-2

-4k+20<6k+6-2

Subtract 2 from 6.

-4k+20<6k+4

-4k+20<6k+4

Subtract 6k from both sides of the inequality.

-4k+20-6k<4

Subtract 6k from -4k.

-10k+20<4

-10k+20<4

Subtract 20 from both sides of the inequality.

-10k<4-20

Subtract 20 from 4.

-10k<-16

-10k<-16

Divide each term in -10k<-16 by -10. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-10k-10>-16-10

Cancel the common factor of -10.

Cancel the common factor.

-10k-10>-16-10

Divide k by 1.

k>-16-10

k>-16-10

Cancel the common factor of -16 and -10.

Factor -2 out of -16.

k>-2(8)-10

Cancel the common factors.

Factor -2 out of -10.

k>-2⋅8-2⋅5

Cancel the common factor.

k>-2⋅8-2⋅5

Rewrite the expression.

k>85

k>85

k>85

k>85

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Graph 4(k+1)-8(k-2)<3(2k+2)-2