Math Problem Statement

shade the values of x on the number line that makes the inqualitiy true. x < -2 or x >6

Solution

To shade the values of xx on the number line that satisfy the inequality x<2x < -2 or x>6x > 6:

  1. Interpret the inequality:

    • x<2x < -2: Values less than 2-2.
    • x>6x > 6: Values greater than 66.
  2. Graphical representation:

    • Shade all points to the left of 2-2 on the number line (not including 2-2).
    • Shade all points to the right of 66 on the number line (not including 66).
  3. Open circles: Since the inequality is strict (<< or >>), use open circles at 2-2 and 66 to indicate these points are not included.

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Relative Questions:

  1. What is the difference between "or" and "and" in inequalities?
  2. How would the graph look if the inequality was x2 or x6x \leq -2 \text{ or } x \geq 6?
  3. What happens if we combine x<2 and x>6x < -2 \text{ and } x > 6 with "and"?
  4. Can you represent x<2 or x>6x < -2 \text{ or } x > 6 as a union of intervals?
  5. How do absolute values relate to inequalities like this one?

Tip: When dealing with "or" inequalities, think about separate regions that don't overlap on the number line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Graphing on a Number Line

Formulas

-

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 6-8