Math Problem Statement
Solution
The graph shows a number line with two open circles, one at and another at . The line is shaded between these two points, indicating that the values of are between and , but do not include and themselves.
To express this range as an absolute value inequality:
This inequality states that the distance of from 0 is less than 7, which matches the shaded region on the graph between and (excluding and themselves).
Would you like more details or have any other questions?
Here are five related questions you might find interesting:
- How would the inequality change if the circles were filled in at and ?
- What would the inequality look like if the range was outside of and ?
- Can you express this inequality as two separate inequalities without using absolute value?
- How would you graph the inequality on a number line?
- What is the general form of an absolute value inequality, and how do you interpret it on a graph?
Tip: When solving absolute value inequalities, always consider the two possible cases (positive and negative) that arise from the definition of absolute value.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Inequalities
Formulas
Absolute Value Inequality: |x| < a
Theorems
Absolute Value Definition
Suitable Grade Level
Grades 7-9