# Solve for x |2x+7|>27 |2x+7|>27
Write |2x+7|>27 as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
2x+7≥0
Solve the inequality.
Subtract 7 from both sides of the inequality.
2x≥-7
Divide each term by 2 and simplify.
Divide each term in 2x≥-7 by 2.
2×2≥-72
Cancel the common factor of 2.
Cancel the common factor.
2×2≥-72
Divide x by 1.
x≥-72
x≥-72
Move the negative in front of the fraction.
x≥-72
x≥-72
x≥-72
In the piece where 2x+7 is non-negative, remove the absolute value.
2x+7>27
To find the interval for the second piece, find where the inside of the absolute value is negative.
2x+7<0
Solve the inequality.
Subtract 7 from both sides of the inequality.
2x<-7
Divide each term by 2 and simplify.
Divide each term in 2x<-7 by 2.
2×2<-72
Cancel the common factor of 2.
Cancel the common factor.
2×2<-72
Divide x by 1.
x<-72
x<-72
Move the negative in front of the fraction.
x<-72
x<-72
x<-72
In the piece where 2x+7 is negative, remove the absolute value and multiply by -1.
-(2x+7)>27
Write as a piecewise.
{2x+7>27x≥-72-(2x+7)>27x<-72
Simplify -(2x+7)>27.
Apply the distributive property.
{2x+7>27x≥-72-(2x)-1⋅7>27x<-72
Multiply 2 by -1.
{2x+7>27x≥-72-2x-1⋅7>27x<-72
Multiply -1 by 7.
{2x+7>27x≥-72-2x-7>27x<-72
{2x+7>27x≥-72-2x-7>27x<-72
{2x+7>27x≥-72-2x-7>27x<-72
Solve 2x+7>27 when x≥-72.
Solve 2x+7>27 for x.
Move all terms not containing x to the right side of the inequality.
Subtract 7 from both sides of the inequality.
2x>27-7
Subtract 7 from 27.
2x>20
2x>20
Divide each term by 2 and simplify.
Divide each term in 2x>20 by 2.
2×2>202
Cancel the common factor of 2.
Cancel the common factor.
2×2>202
Divide x by 1.
x>202
x>202
Divide 20 by 2.
x>10
x>10
x>10
Find the intersection of x>10 and x≥-72.
x>10
x>10
Solve -2x-7>27 when x<-72.
Solve -2x-7>27 for x.
Move all terms not containing x to the right side of the inequality.
Add 7 to both sides of the inequality.
-2x>27+7
Add 27 and 7.
-2x>34
-2x>34
Divide each term by -2 and simplify.
Divide each term in -2x>34 by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-2x-2<34-2
Cancel the common factor of -2.
Cancel the common factor.
-2x-2<34-2
Divide x by 1.
x<34-2
x<34-2
Divide 34 by -2.
x<-17
x<-17
x<-17
Find the intersection of x<-17 and x<-72.
x<-17
x<-17
Find the union of the solutions.
x<-17 or x>10
The result can be shown in multiple forms.
Inequality Form:
x<-17 or x>10
Interval Notation:
(-∞,-17)∪(10,∞)
<div data-graph-input="{"graphs":[{"ascii":"x10","color":0,"isGrey":false,"dashed":false,"holes":[]}],"asymptotes":[],"segments":[],"areaBetweenCurves":[],"points":[],"HasGraphInput":true}” class=”GraphWrapper”>
Solve for x |2x+7|>27

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