Skill: Solve multi-step problems involving integers

When solving a multi-step integer problem:

1. Translate each situation into an integer. Increases are positive; decreases are negative.
2. Write an expression that shows the steps.
3. Use the order of operations: multiplication or division before addition or subtraction.
4. Check whether the answer makes sense in the situation.

Example:
The temperature is $-7^\circ\text{C}$. It rises $12^\circ\text{C}$, then falls $3^\circ\text{C}$ each hour for $4$ hours. What is the final temperature?

A rise of $12$ is $+12$. A fall of $3$ each hour for $4$ hours is $4(-3)$.

Write the expression:

$$-7+12+4(-3)$$

First, multiply:

$$4(-3)=-12$$

Now evaluate from left to right:

$$-7+12+(-12)$$

Combine $-7$ and $12$:

$$-7+12=5$$

Then subtract $12$:

$$5+(-12)=-7$$

So, the final temperature is

$$\boxed{-7^\circ\text{C}}.$$

This is reasonable because the temperature first rises to $5^\circ\text{C}$, then drops $12^\circ\text{C}$, ending at $-7^\circ\text{C}$.