To simplify the given equation \( 2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7 \), we will first simplify the left side using the Distributive Property, and then we will simplify the right side by combining like terms.
Simplifying the left side:
Using the Distributive Property: \[ 2(x - 5) = 2 \cdot x - 2 \cdot 5 = 2x - 10 \]
So, the simplified left side of the equation is: \[ \text{Left side: } 2x - 10 \]
Simplifying the right side:
Now, let's simplify the right side by combining like terms: \[ 9 - 3x + 6 + 8 + 3x + 7 \] First, combine the constant terms: \[ 9 + 6 + 8 + 7 = 30 \] Next, combine the terms involving \( x \): \[ -3x + 3x = 0 \]
So the simplified right side is: \[ \text{Right side: } 30 \]
Final answer:
- Simplified left side: \( 2x - 10 \)
- Simplified right side: \( 30 \)