Math Problem Statement

Write an absolute value inequality for the graph below. Use x for your variable.

Solution

The graph shows a number line with two open circles, one at 7-7 and another at 77. The line is shaded between these two points, indicating that the values of xx are between 7-7 and 77, but do not include 7-7 and 77 themselves.

To express this range as an absolute value inequality:

x<7|x| < 7

This inequality states that the distance of xx from 0 is less than 7, which matches the shaded region on the graph between 7-7 and 77 (excluding 7-7 and 77 themselves).

Would you like more details or have any other questions?

Here are five related questions you might find interesting:

  1. How would the inequality change if the circles were filled in at 7-7 and 77?
  2. What would the inequality look like if the range was outside of 7-7 and 77?
  3. Can you express this inequality as two separate inequalities without using absolute value?
  4. How would you graph the inequality x35|x - 3| \leq 5 on a number line?
  5. 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