To determine if given numbers are solutions to an inequality, you need to substitute each number into the inequality and check if the resulting statement is true. Here's a step-by-step process:
Steps to Check if a Number is a Solution to an Inequality
| Step | Description |
|---|---|
| 1 | Substitute: Replace the variable in the inequality with the given number. |
| 2 | Simplify: Evaluate both sides of the inequality after the substitution. |
| 3 | Determine Truth: Check if the resulting inequality statement is true. |
According to the reference provided:
- Step 1: Substitute the given value of the variable into the inequality.
- Step 2: Simplify both sides of the inequality with the substituted value.
- Step 3: Determine whether the resulting inequality is true. If it is true, then the given value of the variable is a solution to the inequality.
Example
Let's say we want to check if x = 3 is a solution to the inequality 2x + 1 > 5.
- Substitute: Replace x with 3: 2(3) + 1 > 5
- Simplify: Evaluate both sides: 6 + 1 > 5 which simplifies to 7 > 5
- Determine Truth: Is 7 > 5 a true statement? Yes, it is.
Since 7 > 5 is true, x = 3 is a solution to the inequality 2x + 1 > 5.
Another Example
Is x = 1 a solution to the inequality 2x + 1 > 5?
- Substitute: Replace x with 1: 2(1) + 1 > 5
- Simplify: Evaluate both sides: 2 + 1 > 5 which simplifies to 3 > 5
- Determine Truth: Is 3 > 5 a true statement? No, it is not.
Since 3 > 5 is false, x = 1 is not a solution to the inequality 2x + 1 > 5.
