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These sample problems below for Absolute Value Equations were generated by the MathScore.com engine.

## Sample Problems For Absolute Value Equations

### Complexity=1, Mode=simple-eq

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "11 and x<5", "no solution","x=all values"

### Complexity=1, Mode=simple-ineq

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "11 and x<5", "no solution","x=all values"

### Complexity=1, Mode=normal

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "11 and x<5", "no solution","x=all values"
 1.   |3 - x| = 1 Answer: 2.   |3 + x| > 4 Answer:

### Complexity=1, Mode=simple-eq

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "11 and x<5", "no solution","x=all values"
1|x| = 0
2|x| = - 1
Solution
By definition, the absolute value of a number cannot be negative

### Complexity=1, Mode=simple-ineq

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "11 and x<5", "no solution","x=all values"
1|x| < 3
Solution
Remove the absolute value sign, creating two equations, where the absolute value sign is replaced by a -1 in the second equation.
x < 3
-x < 3

Solve both equations to get this:
x < 3
x > - 3

When the first equation is < or <=, x must be valid for both equations (AND expression).
Combine the answers to get this:
-3 < x < 3

2|x| >= 2
Solution
Remove the absolute value sign, creating two equations, where the absolute value sign is replaced by a -1 in the second equation.
x >= 2
-x >= 2

Solve both equations to get this:
x >= 2
x <= - 2

When the first equation is > or >=, x can be valid for either equation (OR expression).
Combine the answers to get this:
x <= -2 or x >= 2

### Complexity=1, Mode=normal

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "11 and x<5", "no solution","x=all values"
1|3 - x| = 1
Solution
Remove the absolute value sign, creating two equations, where the absolute value sign is replaced by a -1 in the second equation.
3 - x = 1
-(3 - x) = 1

Solve both equations to get this:
x = 2
x = 4

Combine the answers to get this:
x = 2,4

2|3 + x| > 4
Solution
Remove the absolute value sign, creating two equations, where the absolute value sign is replaced by a -1 in the second equation.
3 + x > 4
-(3 + x) > 4

Solve both equations to get this:
x > 1
x < - 7

When the first equation is > or >=, x can be valid for either equation (OR expression).
Combine the answers to get this:
x < -7 or x > 1

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