9. For the equation 2(x−5)=9−3x+6+8+3x+7

, the left side of the equation can be simplified using the Distributive Property, and the right side of the equation can be simplified by combining like terms. (2 points)
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Simplify the left side of the equation: Response area

Simplify the right side of the equation: Response area

1 answer

To simplify the left and right sides of the given equation \( 2(x−5)=9−3x+6+8+3x+7 \), we can follow these steps:

Left Side:

  1. Apply the Distributive Property: \[ 2(x - 5) = 2x - 10 \]

Right Side:

  1. Combine like terms: \[ 9 - 3x + 6 + 8 + 3x + 7 \] First, combine the constant terms: \[ 9 + 6 + 8 + 7 = 30 \] Next, combine the \( x \) terms: \[ -3x + 3x = 0 \] So the right side simplifies to: \[ 30 \]

Putting it all together:

Simplified Left Side: \( 2x - 10 \)

Simplified Right Side: \( 30 \)