To justify Step 2 in the solution process, let's look at the transition from Step 1 to Step 2 in detail.
Starting with Step 1:
[tex]\[ -x = 7x + 20 \][/tex]
To eliminate [tex]\(7x\)[/tex] from the right-hand side, you can subtract [tex]\(7x\)[/tex] from both sides of the equation. This operation is performed to isolate the variable [tex]\(x\)[/tex]. Here's the step-by-step process:
1. Subtract [tex]\(7x\)[/tex] from both sides of the equation:
[tex]\[ -x - 7x = 7x + 20 - 7x \][/tex]
2. Combine like terms:
[tex]\[ -8x = 20 \][/tex]
The operation performed—in this case, subtracting [tex]\(7x\)[/tex] from both sides of the equation—is justified by the subtraction property of equality. This property states that if you subtract the same amount from both sides of an equation, the equality is preserved.
Therefore, the correct answer is:
C. the subtraction property of equality
