https://file.aiquickdraw.com/mathbot/file/1726541468896l9wyulfi.jpg

The equation from the image is:

\[
-6(x - 7) = 84
\]

Let's solve this step by step.

### Step 1: Distribute \(-6\) across \((x - 7)\):
\[
-6x + 42 = 84
\]

### Step 2: Subtract 42 from both sides:
\[
-6x = 84 - 42
\]
\[
-6x = 42
\]

### Step 3: Divide both sides by \(-6\) to solve for \(x\):
\[
x = \frac{42}{-6}
\]
\[
x = -7
\]

Thus, the solution to the equation is:

\[
x = -7
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How would the equation change if the number on the right was 100 instead of 84?
2. Can you solve the equation if \(-6\) were replaced by another constant like \(-8\)?
3. What happens if we change the subtraction to addition inside the parentheses?
4. How would you check if \(x = -7\) is the correct solution?
5. How can this approach be extended to solve similar equations?

**Tip:** Always perform inverse operations to isolate the variable step by step!

Learn how to solve the linear equation -6(x - 7) = 84 with a detailed step-by-step solution. This algebraic problem focuses on applying the distributive property and solving for x. Suitable for students in Grades 7-9.

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