If x ≤ -2 or x ≥ 8, then
Understand the Problem
The question is asking to respond appropriately based on given conditions for the variable x, specifically looking for a solution to inequalities involving x. The conditions stated are if x is less than or equal to -2, or if x is greater than or equal to 8.
Answer
The solution to the inequalities is: $$ (-\infty, -2] \cup [8, \infty) $$
Answer for screen readers
The solution to the inequalities is: $$ (-\infty, -2] \cup [8, \infty) $$
Steps to Solve
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Understand the Inequalities We are given two conditions: $x \leq -2$ and $x \geq 8$. We need to analyze the values of $x$ that satisfy either of these conditions.
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Graph the Inequalities On a number line:
- The condition $x \leq -2$ includes all values to the left of and including -2.
- The condition $x \geq 8$ includes all values to the right of and including 8.
- Combine the Solutions Since the problem states "or", we combine the solutions from both inequalities. The solution set consists of:
- All numbers that are less than or equal to -2.
- All numbers that are greater than or equal to 8.
- Final Expression of the Solution The solution can be written in interval notation as: $$ (-\infty, -2] \cup [8, \infty) $$
The solution to the inequalities is: $$ (-\infty, -2] \cup [8, \infty) $$
More Information
This solution represents values of $x$ that fall in either of the specified ranges. The "or" in the inequality indicates that $x$ can belong to either range. This is commonly encountered in problems involving union of intervals in set theory or real analysis.
Tips
- Ignoring the "or" condition: Sometimes, students may mistakenly think they need to find values that satisfy both inequalities simultaneously. Remember "or" means that satisfying either condition is sufficient.
- Incorrect interval notation: Ensure that the intervals are correctly represented, including the use of brackets for inclusive values (like -2 and 8).
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