Answer :
To solve the inequality \(2x < 30\), we'll follow these steps:
1. Understand the inequality: The inequality \(2x < 30\) means we need to find the values of \(x\) that make this statement true.
2. Isolate the variable \(x\): To isolate \(x\), we'll divide both sides of the inequality by 2.
[tex]\[ \frac{2x}{2} < \frac{30}{2} \][/tex]
3. Simplify the inequality: When we divide both sides by 2, it simplifies to:
[tex]\[ x < 15 \][/tex]
4. Interpret the solution: The above simplification shows that \(x\) must be less than 15.
5. Match with the given choices:
- A. \(x > 30\) → This is incorrect because it does not satisfy \(x < 15\).
- B. \(x < 30\) → Although this is true, it is not the most specific answer compared to \(x < 15\).
- C. \(x > 15\) → This is incorrect because it does not satisfy \(x < 15\).
- D. \(x < 15\) → This is correct because it directly satisfies \(x < 15\).
Therefore, the solution to the inequality \(2x < 30\) is:
[tex]\[ \boxed{D. \ x<15} \][/tex]
1. Understand the inequality: The inequality \(2x < 30\) means we need to find the values of \(x\) that make this statement true.
2. Isolate the variable \(x\): To isolate \(x\), we'll divide both sides of the inequality by 2.
[tex]\[ \frac{2x}{2} < \frac{30}{2} \][/tex]
3. Simplify the inequality: When we divide both sides by 2, it simplifies to:
[tex]\[ x < 15 \][/tex]
4. Interpret the solution: The above simplification shows that \(x\) must be less than 15.
5. Match with the given choices:
- A. \(x > 30\) → This is incorrect because it does not satisfy \(x < 15\).
- B. \(x < 30\) → Although this is true, it is not the most specific answer compared to \(x < 15\).
- C. \(x > 15\) → This is incorrect because it does not satisfy \(x < 15\).
- D. \(x < 15\) → This is correct because it directly satisfies \(x < 15\).
Therefore, the solution to the inequality \(2x < 30\) is:
[tex]\[ \boxed{D. \ x<15} \][/tex]
