|2-4x|<10

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.

Subtract 2 from both sides of the inequality.

-4x≥-2

Divide each term by -4 and simplify.

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.

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.

Factor -2 out of -2.

x≤-2(1)-4

Cancel the common factors.

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.

Subtract 2 from both sides of the inequality.

-4x<-2

Divide each term by -4 and simplify.

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.

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.

Factor -2 out of -2.

x>-2(1)-4

Cancel the common factors.

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.

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 for x.

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

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.

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.

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 for x.

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

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.

Divide each term in 4x<12 by 4.

4×4<124

Cancel the common factor of 4.

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

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