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## Absolute Value Equations - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "1<x<5", "x>1 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", "1<x<5", "x>1 and x<5", "no solution","x=all values"

### Complexity=1, Mode=eq

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "1<x<5", "x>1 and x<5", "no solution","x=all values"

 1.   |x - 2| = - 1 Answer: 2.   |x + 3| = 4 Answer:

### Complexity=1, Mode=all

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "1<x<5", "x>1 and x<5", "no solution","x=all values"

 1.   |x + 2| = 2 Answer: 2.   |x - 1| = 4 Answer:

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

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "1<x<5", "x>1 and x<5", "no solution","x=all values"

1|x| = 1
Solution
When you remove the absolute value sign, you get two equations, one where the left side is the original, and one where the left side is multiplied by -1.
Equation 1:
x = 1

Equation 2:
-x = 1
x = - 1
Therefore, we have two answers: x = -1,1

2|x| = 3
Solution
When you remove the absolute value sign, you get two equations, one where the left side is the original, and one where the left side is multiplied by -1.
Equation 1:
x = 3

Equation 2:
-x = 3
x = - 3
Therefore, we have two answers: x = -3,3

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

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "1<x<5", "x>1 and x<5", "no solution","x=all values"

1|x| = 0
Solution
Remove the absolute value sign, creating two equations, where the absolute value sign is replaced by a -1 in the second equation.
x = 0
-x = 0

Solve both equations to get this:
x = 0
x = 0

Combine the answers to get this:
x = 0

2|x| > - 2
Solution
By definition, the absolute value of an expression is never negative, so x=all values

### Complexity=1, Mode=eq

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "1<x<5", "x>1 and x<5", "no solution","x=all values"

1|x - 2| = - 1
Solution
By definition, the absolute value of an expression cannot be negative, so there is no solution.
2|x + 3| = 4
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 = 4
-(x + 3) = 4

Solve both equations to get this:
x = 1
x = - 7

Combine the answers to get this:
x = 1,-7

### Complexity=1, Mode=all

Solve for x. Sample answers: "x=3,-5", "x>5 or x<-3", "1<x<5", "x>1 and x<5", "no solution","x=all values"

1|x + 2| = 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 = 2
-(x + 2) = 2

Solve both equations to get this:
x = 0
x = - 4

Combine the answers to get this:
x = 0,-4

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

Solve both equations to get this:
x = 5
x = - 3

Combine the answers to get this:
x = 5,-3