To solve for the variable in the equation [tex]\( 1 - (x + 2) + 2x = 5(2x - 5) - x \)[/tex], we need to apply the distributive property properly. Let's go through the step-by-step process to determine which equation results from this step.
Firstly, start with the given equation:
[tex]\[ 1 - (x + 2) + 2x = 5(2x - 5) - x \][/tex]
### Left Side Simplification:
Apply the distributive property to eliminate the parentheses:
[tex]\[ 1 - x - 2 + 2x \][/tex]
Combine like terms:
[tex]\[ 1 - 2 - x + 2x \][/tex]
[tex]\[ -1 + x \][/tex]
### Right Side Simplification:
Apply the distributive property on the right-hand side:
[tex]\[ 5(2x - 5) - x \][/tex]
[tex]\[ 10x - 25 - x \][/tex]
Now, putting both sides together, the simplified equation is:
[tex]\[ -1 + x = 10x - 25 - x \][/tex]
Finally, rewrite the equation, aligning similar terms:
[tex]\[ 1 - x - 2 + 2x = 10x - 25 - x \][/tex]
This matches one of the given options. Therefore, the correct answer is:
[tex]\[ 1 - x - 2 + 2x = 10x - 25 - x \][/tex]
Thus, the correct equation resulting from applying the distributive property is:
[tex]\[ \boxed{1 - x - 2 + 2x = 10x - 25 - x} \][/tex]
