Question

Use properties of equality to solve the equation and check your solution.



9(x+3)=−72

Answer 1

To solve the equation \( 9(x + 3) = -72 \), we can follow these steps using properties of equality:

1. **Divide both sides by 9** to isolate the term \( x + 3 \):
\[
x + 3 = \frac{-72}{9}
\]
Simplifying the right side gives:
\[
x + 3 = -8
\]

2. **Subtract 3 from both sides** to solve for \( x \):
\[
x = -8 - 3
\]
Simplifying this gives:
\[
x = -11
\]

### Checking the Solution
We can check the solution by substituting \( x = -11 \) back into the original equation:

1. Substitute \( x \) into the left side of the equation:
\[
9(-11 + 3) = 9(-8)
\]
This simplifies to:
\[
9 \times -8 = -72
\]

2. The left side evaluates to:
\[
-72
\]

Since both sides of the original equation are equal (\(-72 = -72\)), our solution \( x = -11 \) is verified as correct.

### Final Answer
The solution to the equation \( 9(x + 3) = -72 \) is:
\[
\boxed{-11}
\]