The optimal width of a street is 30 feet but it can vary by up to 10 feet. Write an absolute value equation to represent the maximum and minimum widths of the bridge. Let x be represent the width of the street.

The given problem states that the optimal width of a street is 30 feet and it can vary by up to 10 feet, meaning the width can be 10 feet more or 10 feet less than 30 feet. This scenario can be modeled using an absolute value equation.

The absolute value equation representing this situation is:

\[
|x - 30| = 10
\]

Here:
- \( x \) represents the actual width of the street.
- \( 30 \) is the optimal width of the street.
- \( 10 \) represents the allowed variation in either direction (up to 10 feet more or less).

### Solution for the widths:
This equation can be solved by considering two cases:
1. \( x - 30 = 10 \) (the maximum width)
2. \( x - 30 = -10 \) (the minimum width)

Thus:
- For the maximum width: \( x = 30 + 10 = 40 \) feet.
- For the minimum width: \( x = 30 - 10 = 20 \) feet.

So, the street width can vary between 20 and 40 feet.

Would you like further clarification or details?

Here are five related questions to explore further:
1. How would the equation change if the maximum allowed variation were 15 feet?
2. What are other real-life examples where absolute value equations can be used?
3. How do we graph absolute value equations on a number line?
4. How do you solve absolute value inequalities instead of equations?
5. Can you derive an equation with multiple variables involving absolute value?

**Tip:** When solving absolute value equations, always split them into two cases to consider both positive and negative scenarios.

The optimal width of a street is 30 feet but it can vary by up to 10 feet. Write an absolute value equation to represent the maximum and minimum widths of the bridge. Let x represent the width of the street.

Learn how to model the variation in the width of a street using an absolute value equation |x - 30| = 10. This problem explores key algebraic concepts, including absolute value equations and solving for maximum and minimum values. Suitable for students in Grades 7-9.

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