Absolute Value Equations

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•
Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the definition of absolute value?
Back
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.
2.
FLASHCARD QUESTION
Front
What is the general form of an absolute value equation?
Back
An absolute value equation is typically expressed as |A| = B, where A is an expression involving a variable and B is a non-negative number.
3.
FLASHCARD QUESTION
Front
How do you solve the equation |x| = a?
Back
To solve |x| = a, you set up two equations: x = a and x = -a.
4.
FLASHCARD QUESTION
Front
What is the solution to the equation |x - 3| = 5?
Back
The solutions are x = 8 and x = -2.
5.
FLASHCARD QUESTION
Front
What is the graphical representation of an absolute value function?
Back
The graph of an absolute value function is a V-shaped graph that opens upwards.
6.
FLASHCARD QUESTION
Front
How do you solve the equation |2x + 1| = 7?
Back
Set up two equations: 2x + 1 = 7 and 2x + 1 = -7. Solve for x to get x = 3 and x = -4.
7.
FLASHCARD QUESTION
Front
What does it mean if an absolute value equation has no solution?
Back
An absolute value equation has no solution if the expression inside the absolute value cannot equal a negative number.
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