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Questions and Answers
What does the absolute value of a number represent on a number line?
What is the absolute value of -5?
Which of the following absolute value equations has the solutions x = 14 and x = -4?
For which inequality does the solution set include all real numbers except for 5?
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What is the graphical interpretation of the absolute value equation |x - 5| = 9?
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Study Notes
Absolute Value
- The absolute value of a number is the distance the number is from 0 on a number line.
- Absolute value is always positive.
- The absolute value of -5 is 5 because it is 5 units away from zero on the number line.
Solving Simple Absolute Value Equations
- To solve an absolute value equation, isolate the absolute value expression.
- Then, set the expression inside the absolute value bars equal to both the positive and negative value of the number on the other side of the equation and solve for the variable.
- For example, to solve |x - 5| = 9, you would set x - 5 equal to 9 and -9 and solve for x.
Solving Absolute Value Equations
- When solving absolute value equations, it is important to consider both the positive and negative values of the expression inside the absolute value bars.
- For example, to solve |g - 2| = 7, you would set g - 2 equal to 7 and -7 and solve for g.
Solving Inequalities of the form |ax + b| > c
- If |ax + b| > c, then ax + b > c or ax + b < -c
- After rewriting the absolute value inequality into two separate inequalities, solve each one individually..
- For example, to solve |x + 1| >3, you would write it as two separate inequalities: x + 1 > 3 or x + 1 < -3.
- Then, solve each inequality for x to discover the solution.
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Description
Test your understanding of absolute value concepts, including how to find the absolute value of numbers and solve absolute value equations and inequalities. This quiz will challenge you with various problems to reinforce your knowledge and skills in handling absolute values.
