6.AT.C.10 · Unit 0
⚖️ Writing & Solving One-Step Inequalities
Learning goal: I can write and solve one-step inequalities for a context and show the solution set on a number line.
Language goal: I can describe a solution set using the words at least, at most, more than, and less than.
📚 Vocabulary
Inequality: A statement comparing values with >, <, ≥, or ≤.
Solution set: All the values that make an inequality true.
Open / closed circle: Open ○ for > or < (not included); closed ● for ≥ or ≤ (included).
💡 Learn it
An inequality usually has many solutions. Solve it like an equation: undo the operation on both sides.
Example: x + 3 > 7 → x > 4. The solution set is every number greater than 4.
Graph it: open circle at 4 (4 is not included) with an arrow pointing right. Use a closed circle for ≥ or ≤.
Watch the words: 'at least' means ≥, 'at most' means ≤, 'more than' means >, 'fewer/less than' means <.
Worked example. Write and solve: 'A number n plus 5 is at least 12.'
- 'At least 12' means ≥ 12, so n + 5 ≥ 12.
- Subtract 5 from both sides: n ≥ 7.
- Graph: closed circle at 7, arrow to the right.
✏️ Practice
Score: 0 / 5
1. Solve: x + 4 > 9 (write like x > 5 )
💡 Subtract 4 from both sides.
2. Solve: 3x ≤ 12 (write like x <= 4 )
💡 Divide both sides by 3.
3. The graph of x > 2 uses a(n) ___ circle at 2.
💡 > and < do not include the endpoint.
4. 'A number is at least 10' translates to…
💡 'At least' includes the value, so ≥.
5. Is x = 6 a solution of x + 1 > 6 ?
💡 6 + 1 = 7, and 7 > 6 is true.