One-step addition inequalities are mathematical statements that compare two expressions using inequality symbols (>, <, ≥, ≤) and involve adding a constant to a variable. Solving them is similar to solving equations: we isolate the variable by performing the inverse operation (subtraction) on both sides of the inequality. The goal is to find the range of values for the variable that makes the inequality true. For example, in $x + 3 > 5$, we subtract 3 from both sides to get $x > 2$. This means any number greater than 2 will satisfy the original inequality. Remember that what you do to one side of the inequality, you must do to the other to maintain the balance!
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Inequality | A. A value that, when substituted for a variable, makes the inequality true. |
| 2. Variable | B. A mathematical statement that compares two expressions using symbols like >, <, ≥, or ≤. |
| 3. Solution Set | C. A symbol (usually a letter) that represents an unknown number. |
| 4. Constant | D. A fixed value that doesn't change. |
| 5. Inverse Operation | E. The opposite operation used to isolate a variable (e.g., subtraction for addition). |
(Match the terms: 1-?, 2-?, 3-?, 4-?, 5-?)
An inequality is a statement that shows the relationship between two expressions that are not necessarily _____. Solving one-step addition inequalities involves isolating the _____ by using the _____ operation of subtraction. When solving, remember to perform the same operation on _____ sides of the inequality to maintain _____.
Explain in your own words why it's important to perform the same operation on both sides of an inequality when solving it. What happens if you only change one side?
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