To determine if a value is a solution to an inequality, substitute the value for the variable and check if the resulting inequality is true.
Determining if a Value Satisfies an Inequality
The process for checking if a specific value is a solution to an inequality is straightforward. Here's a breakdown:
- Substitution: Replace the variable in the inequality with the given value.
- Simplification: Perform any necessary arithmetic operations to simplify both sides of the inequality.
- Verification: Check if the resulting numerical inequality is true. If it is, the value is a solution; otherwise, it is not.
Reference: To determine whether a given value is a solution to an inequality, we simply need to replace the variable in the inequality with this value and check with the obtained numbers whether the inequality is true or not.
Examples
Let's look at a couple of examples to clarify the process.
Example 1:
Is x = 3 a solution to the inequality 2x + 1 > 5?
- Substitute: Replace x with 3: 2(3) + 1 > 5
- Simplify: 6 + 1 > 5 => 7 > 5
- Verify: Is 7 > 5 true? Yes.
Therefore, x = 3 is a solution to the inequality 2x + 1 > 5.
Example 2:
Is y = -2 a solution to the inequality y - 4 <= -6?
- Substitute: Replace y with -2: -2 - 4 <= -6
- Simplify: -6 <= -6
- Verify: Is -6 <= -6 true? Yes.
Therefore, y = -2 is a solution to the inequality y - 4 <= -6. Note that "less than or equal to" is true when the two values are equal.
Summary Table
| Step | Description |
|---|---|
| 1. Substitute | Replace the variable in the inequality with the value you're testing. |
| 2. Simplify | Perform any calculations to simplify both sides of the inequality. |
| 3. Verify | Check if the resulting numerical inequality is true. |
By following these steps, you can confidently determine whether a given value is a solution to a particular inequality.
