Question

Identify the steps followed to solve the equation 5−3(x+3)=11−8x
(5 points)

5−3x−9=11−8x

−3x−4=11−8x

5x−4=11

5x=15

x=3

Answer 1

To solve the equation \( 5 - 3(x + 3) = 11 - 8x \), we can outline the steps as follows:

1. **Distribute**: Apply the distributive property to expand the left side of the equation.
\[
5 - 3(x + 3) \rightarrow 5 - 3x - 9
\]

2. **Combine like terms**: Simplify the left side by combining the constants.
\[
5 - 9 = -4 \quad \Rightarrow \quad -3x - 4
\]
This gives us:
\[
-3x - 4 = 11 - 8x
\]

3. **Rearrange terms**: Move all terms involving \( x \) to one side and constants to the other side. Add \( 8x \) to both sides.
\[
-3x + 8x - 4 = 11 \quad \Rightarrow \quad 5x - 4 = 11
\]

4. **Isolate the variable**: Add \( 4 \) to both sides to isolate the \( 5x \).
\[
5x = 11 + 4 \quad \Rightarrow \quad 5x = 15
\]

5. **Solve for \( x \)**: Divide both sides by \( 5 \) to find the value of \( x \).
\[
x = \frac{15}{5} \quad \Rightarrow \quad x = 3
\]

Thus, the steps taken to solve the equation \( 5 - 3(x + 3) = 11 - 8x \) result in \( x = 3 \).