Practice
Absolute Value Equations Practice
Fifty original distance, equation, graph, transformation, and solution-count questions.
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Question 1
Explanation
Both \(1\) and \(-1\) are distance \(1\) from zero.
Question 2
Explanation
Both \(2\) and \(-2\) are distance \(2\) from zero.
Question 3
Explanation
Both \(3\) and \(-3\) are distance \(3\) from zero.
Question 4
Explanation
Both \(4\) and \(-4\) are distance \(4\) from zero.
Question 5
Explanation
Both \(5\) and \(-5\) are distance \(5\) from zero.
Question 6
Explanation
Split into \(x--2=2\) and \(x--2=-2\), giving the two stated values.
Question 7
Explanation
Split into \(x--1=3\) and \(x--1=-3\), giving the two stated values.
Question 8
Explanation
Split into \(x-0=4\) and \(x-0=-4\), giving the two stated values.
Question 9
Explanation
Split into \(x-1=5\) and \(x-1=-5\), giving the two stated values.
Question 10
Explanation
Split into \(x-2=6\) and \(x-2=-6\), giving the two stated values.
Question 11
Explanation
Divide by \(2\): \(|x--1|=1\). The positive target creates two branches.
Question 12
Explanation
Divide by \(3\): \(|x-0|=2\). The positive target creates two branches.
Question 13
Explanation
Divide by \(4\): \(|x-1|=3\). The positive target creates two branches.
Question 14
Explanation
Divide by \(5\): \(|x-2|=4\). The positive target creates two branches.
Question 15
Explanation
Divide by \(6\): \(|x-3|=5\). The positive target creates two branches.
Question 16
Explanation
Absolute value cannot equal a negative number.
Question 17
Explanation
Only the inside equal to zero works, producing one solution.
Question 18
Explanation
A positive target produces positive and negative branches.
Question 19
Explanation
Absolute value cannot equal a negative number.
Question 20
Explanation
A positive target produces positive and negative branches.
Question 21
Explanation
The coordinates are \(-2\) and \(2\). Their sum is \(0\).
Question 22
Explanation
The coordinates are \(-2\) and \(4\). Their sum is \(2\).
Question 23
Explanation
The coordinates are \(-2\) and \(6\). Their sum is \(4\).
Question 24
Explanation
The coordinates are \(-2\) and \(8\). Their sum is \(6\).
Question 25
Explanation
The coordinates are \(-2\) and \(10\). Their sum is \(8\).
Question 26
Explanation
The two branches meet at \((h,k)=(-2,-1)\).
Question 27
Explanation
The two branches meet at \((h,k)=(-1,0)\).
Question 28
Explanation
The two branches meet at \((h,k)=(0,1)\).
Question 29
Explanation
The two branches meet at \((h,k)=(1,2)\).
Question 30
Explanation
The two branches meet at \((h,k)=(2,3)\).
Question 31
Explanation
The coefficient \(a=-1\) controls opening direction; its negative sign reflects the V downward.
Question 32
Explanation
The coefficient \(a=-1\) controls opening direction; its negative sign reflects the V downward.
Question 33
Explanation
The coefficient \(a=-1\) controls opening direction; its negative sign reflects the V downward.
Question 34
Explanation
The coefficient \(a=-1\) controls opening direction; its negative sign reflects the V downward.
Question 35
Explanation
The coefficient \(a=-1\) controls opening direction; its negative sign reflects the V downward.
Question 36
Explanation
In \(a|x-h|+k\), the vertex is \((h,k)\). The sign of \(a\) determines opening direction.
Question 37
Explanation
In \(a|x-h|+k\), the vertex is \((h,k)\). The sign of \(a\) determines opening direction.
Question 38
Explanation
In \(a|x-h|+k\), the vertex is \((h,k)\). The sign of \(a\) determines opening direction.
Question 39
Explanation
In \(a|x-h|+k\), the vertex is \((h,k)\). The sign of \(a\) determines opening direction.
Question 40
Explanation
In \(a|x-h|+k\), the vertex is \((h,k)\). The sign of \(a\) determines opening direction.
Question 41
Explanation
Distance between \(x\) and \(10\) is \(|x-10|\), and it equals \(3\).
Question 42
Explanation
Distance between \(x\) and \(11\) is \(|x-11|\), and it equals \(4\).
Question 43
Explanation
Distance between \(x\) and \(12\) is \(|x-12|\), and it equals \(5\).
Question 44
Explanation
Distance between \(x\) and \(13\) is \(|x-13|\), and it equals \(6\).
Question 45
Explanation
Distance between \(x\) and \(14\) is \(|x-14|\), and it equals \(7\).
Question 46
Explanation
Divide by \(3\): \(|x--2|=2\). The solutions are \(-4\) and \(0\), whose sum is \(-4\).
Question 47
Explanation
Divide by \(3\): \(|x--1|=3\). The solutions are \(-4\) and \(2\), whose sum is \(-2\).
Question 48
Explanation
Divide by \(3\): \(|x-0|=4\). The solutions are \(-4\) and \(4\), whose sum is \(0\).
Question 49
Explanation
Divide by \(3\): \(|x-1|=5\). The solutions are \(-4\) and \(6\), whose sum is \(2\).
Question 50
Explanation
Divide by \(3\): \(|x-2|=6\). The solutions are \(-4\) and \(8\), whose sum is \(4\).
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- Question 16Absolute value solution countMedium
- Question 17Absolute value solution countMedium
- Question 18Absolute value solution countMedium
- Question 19Absolute value solution countMedium
- Question 20Absolute value solution countMedium
- Question 21Absolute value distanceMedium
- Question 22Absolute value distanceMedium
- Question 23Absolute value distanceMedium
- Question 24Absolute value distanceMedium
- Question 25Absolute value distanceMedium
- Question 26Absolute value graph vertexMedium
- Question 27Absolute value graph vertexMedium
- Question 28Absolute value graph vertexMedium
- Question 29Absolute value graph vertexMedium
- Question 30Absolute value graph vertexMedium
- Question 31Absolute value graph behaviorMedium
- Question 32Absolute value graph behaviorMedium
- Question 33Absolute value graph behaviorMedium
- Question 34Absolute value graph behaviorMedium
- Question 35Absolute value graph behaviorMedium
- Question 36Absolute value transformationsMedium
- Question 37Absolute value transformationsMedium
- Question 38Absolute value transformationsMedium
- Question 39Absolute value transformationsMedium
- Question 40Absolute value transformationsMedium
- Question 41Model absolute value distanceHard
- Question 42Model absolute value distanceHard
- Question 43Model absolute value distanceHard
- Question 44Model absolute value distanceHard
- Question 45Model absolute value distanceHard
- Question 46Absolute value solution symmetryHard
- Question 47Absolute value solution symmetryHard
- Question 48Absolute value solution symmetryHard
- Question 49Absolute value solution symmetryHard
- Question 50Absolute value solution symmetryHard