|5-2x|>11

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

5-2x≥0

Solve the inequality.

Subtract 5 from both sides of the inequality.

-2x≥-5

Divide each term by -2 and simplify.

Divide each term in -2x≥-5 by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-2x-2≤-5-2

Cancel the common factor of -2.

Cancel the common factor.

-2x-2≤-5-2

Divide x by 1.

x≤-5-2

x≤-5-2

Dividing two negative values results in a positive value.

x≤52

x≤52

x≤52

In the piece where 5-2x is non-negative, remove the absolute value.

5-2x>11

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

5-2x<0

Solve the inequality.

Subtract 5 from both sides of the inequality.

-2x<-5

Divide each term by -2 and simplify.

Divide each term in -2x<-5 by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-2x-2>-5-2

Cancel the common factor of -2.

Cancel the common factor.

-2x-2>-5-2

Divide x by 1.

x>-5-2

x>-5-2

Dividing two negative values results in a positive value.

x>52

x>52

x>52

In the piece where 5-2x is negative, remove the absolute value and multiply by -1.

-(5-2x)>11

Write as a piecewise.

{5-2x>11x≤52-(5-2x)>11x>52

Simplify -(5-2x)>11.

Apply the distributive property.

{5-2x>11x≤52-1⋅5-(-2x)>11x>52

Multiply -1 by 5.

{5-2x>11x≤52-5-(-2x)>11x>52

Multiply -2 by -1.

{5-2x>11x≤52-5+2x>11x>52

{5-2x>11x≤52-5+2x>11x>52

{5-2x>11x≤52-5+2x>11x>52

Solve 5-2x>11 for x.

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

Subtract 5 from both sides of the inequality.

-2x>11-5

Subtract 5 from 11.

-2x>6

-2x>6

Divide each term by -2 and simplify.

Divide each term in -2x>6 by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-2x-2<6-2

Cancel the common factor of -2.

Cancel the common factor.

-2x-2<6-2

Divide x by 1.

x<6-2

x<6-2

Divide 6 by -2.

x<-3

x<-3

x<-3

Find the intersection of x<-3 and x≤52.

x<-3

x<-3

Solve -5+2x>11 for x.

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

Add 5 to both sides of the inequality.

2x>11+5

Add 11 and 5.

2x>16

2x>16

Divide each term by 2 and simplify.

Divide each term in 2x>16 by 2.

2×2>162

Cancel the common factor of 2.

Cancel the common factor.

2×2>162

Divide x by 1.

x>162

x>162

Divide 16 by 2.

x>8

x>8

x>8

Find the intersection of x>8 and x>52.

x>8

x>8

Find the union of the solutions.

x<-3 or x>8

The result can be shown in multiple forms.

Inequality Form:

x<-3 or x>8

Interval Notation:

(-∞,-3)∪(8,∞)

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