📚 Topic Summary
Inequalities are like equations, but instead of an equals sign (=), they use symbols like > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to). Solving one-step inequalities by subtracting involves isolating the variable on one side of the inequality. To do this, you subtract the same number from both sides of the inequality, making sure to keep the inequality balanced. The solution will be a range of values instead of a single value.
🔤 Part A: Vocabulary
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 symbol (usually a letter) that represents an unknown value. |
| 3. Solution Set |
C. A statement that compares two expressions using symbols like >, <, ≥, or ≤. |
| 4. Isolate |
D. To get the variable by itself on one side of the inequality. |
| 5. Subtract |
E. To take away a number or quantity from another. |
(Answers: 1-C, 2-B, 3-A, 4-D, 5-E)
📝 Part B: Fill in the Blanks
To solve the inequality $x + 5 > 10$, we need to _______ 5 from both sides. This will _______ the variable $x$ on the left side of the inequality. After subtracting, we get $x >$ _______. This means that $x$ is greater than _______. The _______ _______ consists of all numbers greater than that number.
(Answers: subtract, isolate, 5, 5, solution set)
🤔 Part C: Critical Thinking
Explain in your own words why we can subtract the same number from both sides of an inequality without changing the solution set.