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.

Question

Simplify the left side of the equation: ____________
Simplify the right side of the equation: ____________
Options: 36x, 30, 2x - 5, 30x, 6x + 30, 2x - 10

Answer 1

Let's simplify both sides of the equation step-by-step.

Left Side: The left side of the equation is \( 2(x - 5) \).

Using the Distributive Property: \[ 2(x - 5) = 2 \cdot x - 2 \cdot 5 = 2x - 10 \]

Right Side: The right side of the equation is: \( 9 - 3x + 6 + 8 + 3x + 7 \).

First, we can add together the constant terms: \[ 9 + 6 + 8 + 7 = 30 \]

Now, combining the \( -3x \) and \( +3x \): \[ -3x + 3x = 0 \]

Thus, the right side simplifies to: \[ 30 \]

Final Answers:

• Simplified Left Side: \( 2x - 10 \)
• Simplified Right Side: \( 30 \)

So:

• Simplify the left side of the equation: 2x - 10
• Simplify the right side of the equation: 30

Answer 2

are you sure this answer is correct

Answer 3

Let's verify the simplifications again for clarity.

Left Side

The left side of the equation is: \[ 2(x - 5) \]

Applying the Distributive Property: \[ 2(x - 5) = 2 \cdot x - 2 \cdot 5 = 2x - 10 \] This simplification is correct.

Right Side

The right side of the equation is: \[ 9 - 3x + 6 + 8 + 3x + 7 \]

Now let's combine the constant terms and the \(x\) terms separately.

First, let's combine the constant numbers: \[ 9 + 6 + 8 + 7 = 30 \]

Next, combine the terms with \(x\): \[ -3x + 3x = 0 \]

So, after simplifying, the right side becomes: \[ 30 \]

Summary of Simplifications

• Left Side simplifies to: 2x - 10
• Right Side simplifies to: 30

Thus, the previous conclusion is indeed correct. If you have any specific concerns or further questions, please let me know!