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To solve this problem, let's analyze both parts step by step:

### Part (a)
The problem asks for the expression that gives the amount by which the balance increases after the deposit. The balance before the deposit is \(-39\) dollars, and after the deposit, the balance is \(14\) dollars.

The increase in balance can be found by calculating the difference between the balance after the deposit and the balance before the deposit:
\[
\text{Increase} = \text{after deposit} - \text{before deposit} = 14 - (-39)
\]

This is equivalent to adding \(14\) to \(39\), so the correct expression is:
\[
39 + 14
\]
However, since the options are all set with the negative sign applied to 39 and 14, the correct choice for the expression based on the given options is:
\[
-(-39) + 14
\]
which simplifies to:
\[
39 + 14
\]

### Part (b)
Using the expression from part (a), the increase in the balance is:
\[
39 + 14 = 53
\]

### Answers
- **Part (a):** The correct expression is \( -(-39) + 14 \).
- **Part (b):** The balance increases by **53 dollars**.

Would you like any further details or have any questions? Here are a few related questions to consider:

1. How do you subtract a negative number from another number?
2. What is the difference between adding and subtracting in terms of operations on a number line?
3. How can we visualize the addition and subtraction of integers on a number line?
4. How do we determine the sign of the result when adding or subtracting integers?
5. What is the significance of absolute value in this context?

**Tip:** When subtracting a negative number, remember that it is the same as adding the absolute value of that number.

Melissa deposits money into a bank account. The balances (in dollars) before and after the deposit are shown on the number line. (a) Choose the expression that gives how much the balance increases after the deposit. (b) Using your answer from part (a), how much did the balance increase after the deposit?

Learn how to calculate the balance increase after a deposit using integer operations and absolute value. This problem involves understanding how to handle negative numbers and addition in the context of bank account balances. Suitable for students in Grades 6-7.

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