https://file.aiquickdraw.com/mathbot/file/172653770579312vf4f05.jpg

The expression presented in the image is:

\[
5(t - 7) - (t - 3)
\]

We need to clear the parentheses and combine like terms. Let's solve this step by step:

### Step 1: Distribute the constants.
Distribute the **5** to both terms inside the parentheses:

\[
5(t - 7) = 5t - 35
\]

Now distribute the **negative sign (-)** to the terms inside the second parentheses:

\[
-(t - 3) = -t + 3
\]

### Step 2: Combine the expressions.
Now, the expression becomes:

\[
5t - 35 - t + 3
\]

### Step 3: Combine like terms.
Combine the terms with **t** and the constant terms:

\[
(5t - t) + (-35 + 3) = 4t - 32
\]

### Final Answer:
\[
4t - 32
\]

Would you like any further explanation or details on this?

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Here are 5 related questions to explore:

1. How would you simplify an expression like \( 7(t + 2) - 3(t - 1) \)?
2. What happens when you distribute a negative sign across parentheses?
3. How do you combine like terms with different coefficients?
4. What are the steps to solving an equation with parentheses on both sides?
5. How can simplifying expressions help in solving algebraic equations?

**Tip:** Always ensure that you distribute any negative signs carefully when simplifying expressions, as mistakes here are common.

Clear parentheses and combine like terms: 5(t - 7) - (t - 3)

Learn how to simplify the expression 5(t - 7) - (t - 3) by applying the distributive property and combining like terms. This solution covers key algebra concepts suitable for students in Grades 7-9.

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