"Identifying solutions to a one-step linear inequality"

Introduction to One-Step Linear Inequalities

Definition: A one-step linear inequality is an inequality in which you can isolate the variable in one step.
Purpose: The goal is to determine if a particular value for the variable satisfies (or makes true) the inequality.

Key Concepts

Solution of Inequality: A solution to the inequality is a value that results in a true statement when substituted into the inequality.

Example Inequality

Given Inequality:
- x (let's say x = value)
- 56 ≥ 45 + x

Steps to Determine if a Value is a Solution

Substitution: Replace x with the given value in the inequality.
Simplification: Perform necessary arithmetic to simplify the inequality and determine its truth value.
Conclusion: If the resulting statement is true, then that value is a solution. If false, it is not a solution.

Worked Examples

For x = 9:
- Substitute into the inequality:
  56 ≥ 45 + 9
  56 ≥ 54
- Result: True, hence x = 9 is a solution.
For x = 7:
- Substitute:
  56 ≥ 45 + 7
  56 ≥ 52
- Result: True, hence x = 7 is a solution.
For x = 14:
- Substitute:
  56 ≥ 45 + 14
  56 ≥ 59
- Result: False, hence x = 14 is NOT a solution.
For x = 11:
- Substitute:
  56 ≥ 45 + 11
  56 ≥ 56
- Result: True, hence x = 11 is a solution.

Summary of Results

Check your substitution process:
- For x = 9: True
- For x = 7: True
- For x = 14: False
- For x = 11: True

Final Notes

Always ensure to simplify correctly and check each step to accurately determine solutions to inequalities.
Practice with other values and inequalities to become proficient at identifying solutions successfully.