Question

Solve this problem by writing and solving an inequality. Five more than four times a number is less than 25. What are the possible values of the number? Show your work. (4 points) write it like a human 7th grader would with semi-formal grammar

Answer 1

To solve the problem, we need to create an inequality based on the information given. The problem says that "five more than four times a number is less than 25."

Let’s break this down step by step:

1. **Define the number**: We'll call the number \( x \).

2. **Translate the phrase into an inequality**:
- "Four times a number" means \( 4x \).
- "Five more than four times a number" means \( 4x + 5 \).
- "Is less than 25" means we use the less than symbol: \( < 25 \).

Putting it all together, we can write the inequality as:
\[ 4x + 5 < 25. \]

3. **Solve the inequality**:
- First, we want to get rid of the 5 on the left side. We do this by subtracting 5 from both sides:
\[ 4x + 5 - 5 < 25 - 5, \]
which simplifies to:
\[ 4x < 20. \]

- Next, we need to solve for \( x \) by dividing both sides by 4:
\[ \frac{4x}{4} < \frac{20}{4}, \]
which simplifies to:
\[ x < 5. \]

4. **Conclusion**:
So the solution to the inequality \( x < 5 \) means that the possible values of the number \( x \) can be any number that is less than 5. This could be 4, 3, 2, 1, 0, and even negative numbers.

In summary, the possible values of the number are all numbers less than 5!