|6w+2|-6>8

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

6w+2≥0

Solve the inequality.

Subtract 2 from both sides of the inequality.

6w≥-2

Divide each term by 6 and simplify.

Divide each term in 6w≥-2 by 6.

6w6≥-26

Cancel the common factor of 6.

Cancel the common factor.

6w6≥-26

Divide w by 1.

w≥-26

w≥-26

Simplify -26.

Cancel the common factor of -2 and 6.

Factor 2 out of -2.

w≥2(-1)6

Cancel the common factors.

Factor 2 out of 6.

w≥2⋅-12⋅3

Cancel the common factor.

w≥2⋅-12⋅3

Rewrite the expression.

w≥-13

w≥-13

w≥-13

Move the negative in front of the fraction.

w≥-13

w≥-13

w≥-13

w≥-13

In the piece where 6w+2 is non-negative, remove the absolute value.

6w+2-6>8

To find the interval for the second piece, find where the inside of the absolute value is negative.

6w+2<0

Solve the inequality.

Subtract 2 from both sides of the inequality.

6w<-2

Divide each term by 6 and simplify.

Divide each term in 6w<-2 by 6.

6w6<-26

Cancel the common factor of 6.

Cancel the common factor.

6w6<-26

Divide w by 1.

w<-26

w<-26

Simplify -26.

Cancel the common factor of -2 and 6.

Factor 2 out of -2.

w<2(-1)6

Cancel the common factors.

Factor 2 out of 6.

w<2⋅-12⋅3

Cancel the common factor.

w<2⋅-12⋅3

Rewrite the expression.

w<-13

w<-13

w<-13

Move the negative in front of the fraction.

w<-13

w<-13

w<-13

w<-13

In the piece where 6w+2 is negative, remove the absolute value and multiply by -1.

-(6w+2)-6>8

Write as a piecewise.

{6w+2-6>8w≥-13-(6w+2)-6>8w<-13

Subtract 6 from 2.

{6w-4>8w≥-13-(6w+2)-6>8w<-13

Simplify -(6w+2)-6>8.

Simplify each term.

Apply the distributive property.

{6w-4>8w≥-13-(6w)-1⋅2-6>8w<-13

Multiply 6 by -1.

{6w-4>8w≥-13-6w-1⋅2-6>8w<-13

Multiply -1 by 2.

{6w-4>8w≥-13-6w-2-6>8w<-13

{6w-4>8w≥-13-6w-2-6>8w<-13

Subtract 6 from -2.

{6w-4>8w≥-13-6w-8>8w<-13

{6w-4>8w≥-13-6w-8>8w<-13

{6w-4>8w≥-13-6w-8>8w<-13

Solve 6w-4>8 for w.

Move all terms not containing w to the right side of the inequality.

Add 4 to both sides of the inequality.

6w>8+4

Add 8 and 4.

6w>12

6w>12

Divide each term by 6 and simplify.

Divide each term in 6w>12 by 6.

6w6>126

Cancel the common factor of 6.

Cancel the common factor.

6w6>126

Divide w by 1.

w>126

w>126

Divide 12 by 6.

w>2

w>2

w>2

Find the intersection of w>2 and w≥-13.

w>2

w>2

Solve -6w-8>8 for w.

Move all terms not containing w to the right side of the inequality.

Add 8 to both sides of the inequality.

-6w>8+8

Add 8 and 8.

-6w>16

-6w>16

Divide each term by -6 and simplify.

Divide each term in -6w>16 by -6. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-6w-6<16-6

Cancel the common factor of -6.

Cancel the common factor.

-6w-6<16-6

Divide w by 1.

w<16-6

w<16-6

Simplify 16-6.

Cancel the common factor of 16 and -6.

Factor 2 out of 16.

w<2(8)-6

Cancel the common factors.

Factor 2 out of -6.

w<2⋅82⋅-3

Cancel the common factor.

w<2⋅82⋅-3

Rewrite the expression.

w<8-3

w<8-3

w<8-3

Move the negative in front of the fraction.

w<-83

w<-83

w<-83

w<-83

Find the intersection of w<-83 and w<-13.

w<-83

w<-83

Find the union of the solutions.

w<-83 or w>2

The result can be shown in multiple forms.

Inequality Form:

w<-83 or w>2

Interval Notation:

(-∞,-83)∪(2,∞)

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