Answer:
addition property of equality
Explanation:
You want the justification for step 1 in the solution process for -22 - x = 14 + 6x.
Solution
No solution process steps are shown, but we can speculate what they might be.
The goal is to separate constant terms and variable terms. This can be done several ways, but generally consists of adding the same thing to both sides of the equation.
Often, you're told to collect the variable terms first. Some prefer to do that so the variable terms are on the left side of the equal sign. Others prefer to do that so the result has a positive coefficient for the variable term. Taking the latter tack, we want to add x (the opposite of -x) to both sides of the equation:
-22 -x +x = 14 +6x +x . . . . . x added to both sides
-22 = 14 +7x . . . . . . . simplified
The justification for this step is the addition property of equality. That property allows you to add the same thing to both sides of an equation without changing the values of the variables.
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Additional comment
Step 2 would be to add -14 to both sides, giving you ...
-36 = 7x . . . . . . . . add -14; addition property of equality
If you like, you can do both of these additions in one step:
-22 -x +(x -14) = 14 +6x +(x -14) . . . add(x -14); addition property of equality
-36 = 7x . . . . . . simplified
Step 3 is to divide by the coefficient of the variable.
-36/7 = (7x)/7 . . . . division property of equality
-5 1/7 = x . . . . . . . simplified. This is the solution.
The usual procedure takes 3 steps, so this is called a "3-step equation."
Note that we choose for the variable coefficient to be positive, because we judge arithmetic with positive numbers to be less error-prone. If you collect the variable terms on the left, you get ...
-7x = 36
so have to divide by -7. This should not be an issue if you're careful with your arithmetic, but many find dealing with negative numbers to be a challenge.