# Solve for x |5-2x|>11 |5-2x|>11
Write |5-2x|>11 as a piecewise.
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 when x≤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 when x>52.
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,∞)
<div data-graph-input="{"graphs":[{"ascii":"x8","color":0,"isGrey":false,"dashed":false,"holes":[]}],"asymptotes":[],"segments":[],"areaBetweenCurves":[],"points":[],"HasGraphInput":true}” class=”GraphWrapper”>
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