In order to solve for the variable in the equation 1 minus (x + 2) + 2 x = 5 (2 x minus 5) minus x, Mikel first applies the distributive property. Which equation is a result of this step?

Question

1 minus x + 2 + 2 x = 10 x minus 5 minus x
1 minus x minus 2 + 2 x = 10 x minus 25 minus x
1 minus x minus 1 + 2 x = 10 x minus 25 minus x
1 minus x minus 1 + 2 x = 10 x minus 5 minus x

Answer 1

To apply the distributive property to the equation \( 1 - (x + 2) + 2x = 5(2x - 5) - x \), we will first simplify both sides step by step.

Starting with the left side:

• Distribute the negative sign: \[ 1 - (x + 2) + 2x = 1 - x - 2 + 2x \]
• Combine like terms: \[ 1 - 2 - x + 2x = -1 + x \]

Now, focusing on the right side:

• Distribute the \( 5 \): \[ 5(2x - 5) - x = 10x - 25 - x \]
• Combine like terms: \[ 10x - x - 25 = 9x - 25 \]

Putting it all together, after applying the distributive property, we have: \[ -1 + x = 9x - 25 \]

Thus, the equation that results from applying the distributive property is: \[ 1 - x - 1 + 2x = 10x - 25 - x \]

So the correct option that represents the result after applying the distributive property is: \[ 1 - x - 1 + 2x = 10x - 25 - x \]