Absolute Value Equations Sample Problems

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

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"

#	Problem	Correct Answer	Your Answer
1	\|x\| = 0	Answer:

#	Problem	Correct Answer	Your Answer
2	\|x\| = ^-1	Answer:
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"

#	Problem	Correct Answer	Your Answer
1	\|x\| < 3	Answer:
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

Problem

Correct Answer

Your Answer

|x| < 3

Answer:

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

#	Problem	Correct Answer	Your Answer
2	\|x\| >= 2	Answer:
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

Problem

Correct Answer

Your Answer

|x| >= 2

Answer:

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"

#	Problem	Correct Answer	Your Answer
1	\|3 - x\| = 1	Answer:
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

Problem

Correct Answer

Your Answer

|3 - x| = 1

Answer:

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

#	Problem	Correct Answer	Your Answer
2	\|3 + x\| > 4	Answer:
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

Problem

Correct Answer

Your Answer

|3 + x| > 4

Answer:

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

MathScore.com

Sample Problems For Absolute Value Equations

Complexity=1, Mode=simple-eq

Complexity=1, Mode=simple-ineq

Complexity=1, Mode=normal

Answers

Complexity=1, Mode=simple-eq

Complexity=1, Mode=simple-ineq

Complexity=1, Mode=normal