Graph |2-4x|<10

Math
|2-4x|<10
Write |2-4x|<10 as a piecewise.
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To find the interval for the first piece, find where the inside of the absolute value is non-negative.
2-4x≥0
Solve the inequality.
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Subtract 2 from both sides of the inequality.
-4x≥-2
Divide each term by -4 and simplify.
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Divide each term in -4x≥-2 by -4. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-4x-4≤-2-4
Cancel the common factor of -4.
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Cancel the common factor.
-4x-4≤-2-4
Divide x by 1.
x≤-2-4
x≤-2-4
Cancel the common factor of -2 and -4.
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Factor -2 out of -2.
x≤-2(1)-4
Cancel the common factors.
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Factor -2 out of -4.
x≤-2⋅1-2⋅2
Cancel the common factor.
x≤-2⋅1-2⋅2
Rewrite the expression.
x≤12
x≤12
x≤12
x≤12
x≤12
In the piece where 2-4x is non-negative, remove the absolute value.
2-4x<10
To find the interval for the second piece, find where the inside of the absolute value is negative.
2-4x<0
Solve the inequality.
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Subtract 2 from both sides of the inequality.
-4x<-2
Divide each term by -4 and simplify.
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Divide each term in -4x<-2 by -4. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-4x-4>-2-4
Cancel the common factor of -4.
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Cancel the common factor.
-4x-4>-2-4
Divide x by 1.
x>-2-4
x>-2-4
Cancel the common factor of -2 and -4.
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Factor -2 out of -2.
x>-2(1)-4
Cancel the common factors.
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Factor -2 out of -4.
x>-2⋅1-2⋅2
Cancel the common factor.
x>-2⋅1-2⋅2
Rewrite the expression.
x>12
x>12
x>12
x>12
x>12
In the piece where 2-4x is negative, remove the absolute value and multiply by -1.
-(2-4x)<10
Write as a piecewise.
{2-4x<10x≤12-(2-4x)<10x>12
Simplify -(2-4x)<10.
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Apply the distributive property.
{2-4x<10x≤12-1⋅2-(-4x)<10x>12
Multiply -1 by 2.
{2-4x<10x≤12-2-(-4x)<10x>12
Multiply -4 by -1.
{2-4x<10x≤12-2+4x<10x>12
{2-4x<10x≤12-2+4x<10x>12
{2-4x<10x≤12-2+4x<10x>12
Solve 2-4x<10 when x≤12.
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Solve 2-4x<10 for x.
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Move all terms not containing x to the right side of the inequality.
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Subtract 2 from both sides of the inequality.
-4x<10-2
Subtract 2 from 10.
-4x<8
-4x<8
Divide each term by -4 and simplify.
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Divide each term in -4x<8 by -4. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-4x-4>8-4
Cancel the common factor of -4.
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Cancel the common factor.
-4x-4>8-4
Divide x by 1.
x>8-4
x>8-4
Divide 8 by -4.
x>-2
x>-2
x>-2
Find the intersection of x>-2 and x≤12.
-2<x≤12
-2<x≤12
Solve -2+4x<10 when x>12.
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Solve -2+4x<10 for x.
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Move all terms not containing x to the right side of the inequality.
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Add 2 to both sides of the inequality.
4x<10+2
Add 10 and 2.
4x<12
4x<12
Divide each term by 4 and simplify.
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Divide each term in 4x<12 by 4.
4×4<124
Cancel the common factor of 4.
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Cancel the common factor.
4×4<124
Divide x by 1.
x<124
x<124
Divide 12 by 4.
x<3
x<3
x<3
Find the intersection of x<3 and x>12.
12<x<3
12<x<3
Find the union of the solutions.
-2<x<3
<div data-graph-input="{"graphs":[{"ascii":"-2<x
Graph |2-4x|<10

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