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

Math
4(k+1)-8(k-2)<3(2k+2)-2
Simplify 4(k+1)-8(k-2).
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Simplify each term.
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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.
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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 3(2k+2)-2.
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Simplify each term.
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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
Move all terms containing k to the left side of the inequality.
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Subtract 6k from both sides of the inequality.
-4k+20-6k<4
Subtract 6k from -4k.
-10k+20<4
-10k+20<4
Move all terms not containing k to the right side of the inequality.
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Subtract 20 from both sides of the inequality.
-10k<4-20
Subtract 20 from 4.
-10k<-16
-10k<-16
Divide each term by -10 and simplify.
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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.
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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.
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Factor -2 out of -16.
k>-2(8)-10
Cancel the common factors.
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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

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