What does it mean for a number to be a solution to an inequality?

A number is considered a **solution to an inequality** if, when substituted into the inequality, it makes the inequality a true statement. In other words, the number satisfies the condition specified by the inequality.

For example, consider the inequality:

\[
x + 2 < 5
\]

To determine whether a number, say \( x = 2 \), is a solution, substitute it into the inequality:

\[
2 + 2 < 5
\]

Since \( 4 < 5 \) is true, \( x = 2 \) is a solution to the inequality.

If substituting a number makes the inequality false, that number is **not** a solution. For instance, if we try \( x = 4 \):

\[
4 + 2 < 5 \implies 6 < 5
\]

This statement is false, so \( x = 4 \) is not a solution.

### Key Points:
- A solution satisfies the inequality.
- It can be part of a set of numbers that make the inequality true.
- Solutions are often represented as intervals on a number line or in set notation.

Would you like more details on solving inequalities or how to graph the solutions?

### 5 Related Questions:
1. How do you solve a compound inequality?
2. What are the rules for reversing inequalities?
3. How do inequalities differ from equations?
4. What is interval notation, and how is it used in inequalities?
5. How do you graph solutions to inequalities on a number line?

**Tip:** When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign.

Learn what it means for a number to be a solution to an inequality with examples such as x + 2 < 5. Understand how to test if a number satisfies the inequality and explore key concepts like inequality reversal when multiplying or dividing by negative numbers. Suitable for Grades 6-8.

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