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

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

GPT-4o mini · Answer

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 $.