five times the quantity of a number increased by six is no less than one hundred.translate and solve

The problem can be translated into a mathematical inequality as follows:

**Step 1: Translate the problem into an equation.**
- Let the unknown number be \( x \).
- "Five times the quantity of a number increased by six" translates to \( 5(x + 6) \).
- "Is no less than" indicates a "greater than or equal to" relationship (≥).
- "One hundred" translates to 100.

So the inequality is:

\[
5(x + 6) \geq 100
\]

**Step 2: Solve the inequality.**
1. Distribute the 5 on the left-hand side:
   \[
   5x + 30 \geq 100
   \]
2. Subtract 30 from both sides:
   \[
   5x \geq 70
   \]
3. Divide both sides by 5:
   \[
   x \geq 14
   \]

**Final Answer:**
The solution is \( x \geq 14 \).

This means that the number must be at least 14.

Would you like more details or have any questions about this solution?

### Related Questions:
1. What is the difference between solving an equation and solving an inequality?
2. How do you graph the solution \( x \geq 14 \) on a number line?
3. What happens if the inequality had been "no more than 100" instead of "no less than 100"?
4. How would the solution change if the problem involved division instead of multiplication?
5. What are some real-world scenarios where inequalities like this might be used?

### Tip:
Always check your solution by substituting it back into the original inequality to ensure it satisfies the condition.

Learn how to solve the inequality "Five times the quantity of a number increased by six is no less than one hundred" with a detailed step-by-step solution. This problem covers basic algebraic concepts, including inequalities and solving equations. Suitable for students in Grades 7-9.

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