Graph |10-4x|<13

Math
|10-4x|<13
Write |10-4x|<13 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.
10-4x≥0
Solve the inequality.
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Subtract 10 from both sides of the inequality.
-4x≥-10
Divide each term by -4 and simplify.
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Divide each term in -4x≥-10 by -4. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-4x-4≤-10-4
Cancel the common factor of -4.
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Cancel the common factor.
-4x-4≤-10-4
Divide x by 1.
x≤-10-4
x≤-10-4
Cancel the common factor of -10 and -4.
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Factor -2 out of -10.
x≤-2(5)-4
Cancel the common factors.
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Factor -2 out of -4.
x≤-2⋅5-2⋅2
Cancel the common factor.
x≤-2⋅5-2⋅2
Rewrite the expression.
x≤52
x≤52
x≤52
x≤52
x≤52
In the piece where 10-4x is non-negative, remove the absolute value.
10-4x<13
To find the interval for the second piece, find where the inside of the absolute value is negative.
10-4x<0
Solve the inequality.
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Subtract 10 from both sides of the inequality.
-4x<-10
Divide each term by -4 and simplify.
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Divide each term in -4x<-10 by -4. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-4x-4>-10-4
Cancel the common factor of -4.
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Cancel the common factor.
-4x-4>-10-4
Divide x by 1.
x>-10-4
x>-10-4
Cancel the common factor of -10 and -4.
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Factor -2 out of -10.
x>-2(5)-4
Cancel the common factors.
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Factor -2 out of -4.
x>-2⋅5-2⋅2
Cancel the common factor.
x>-2⋅5-2⋅2
Rewrite the expression.
x>52
x>52
x>52
x>52
x>52
In the piece where 10-4x is negative, remove the absolute value and multiply by -1.
-(10-4x)<13
Write as a piecewise.
{10-4x<13x≤52-(10-4x)<13x>52
Simplify -(10-4x)<13.
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Apply the distributive property.
{10-4x<13x≤52-1⋅10-(-4x)<13x>52
Multiply -1 by 10.
{10-4x<13x≤52-10-(-4x)<13x>52
Multiply -4 by -1.
{10-4x<13x≤52-10+4x<13x>52
{10-4x<13x≤52-10+4x<13x>52
{10-4x<13x≤52-10+4x<13x>52
Solve 10-4x<13 when x≤52.
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Solve 10-4x<13 for x.
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Move all terms not containing x to the right side of the inequality.
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Subtract 10 from both sides of the inequality.
-4x<13-10
Subtract 10 from 13.
-4x<3
-4x<3
Divide each term by -4 and simplify.
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Divide each term in -4x<3 by -4. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-4x-4>3-4
Cancel the common factor of -4.
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Cancel the common factor.
-4x-4>3-4
Divide x by 1.
x>3-4
x>3-4
Move the negative in front of the fraction.
x>-34
x>-34
x>-34
Find the intersection of x>-34 and x≤52.
-34<x≤52
-34<x≤52
Solve -10+4x<13 when x>52.
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Solve -10+4x<13 for x.
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Move all terms not containing x to the right side of the inequality.
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Add 10 to both sides of the inequality.
4x<13+10
Add 13 and 10.
4x<23
4x<23
Divide each term by 4 and simplify.
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Divide each term in 4x<23 by 4.
4×4<234
Cancel the common factor of 4.
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Cancel the common factor.
4×4<234
Divide x by 1.
x<234
x<234
x<234
x<234
Find the intersection of x<234 and x>52.
52<x<234
52<x<234
Find the union of the solutions.
-34<x<234
<div data-graph-input="{"graphs":[{"ascii":"-(3)/(4)<x
Graph |10-4x|<13

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