Answer :
To determine the justification for Step 1 in the solution process, let's look at the original equation:
[tex]\[ -22 - x = 5 + 6x + 9 \][/tex]
Step 1 simplifies the right side of the equation:
[tex]\[ -22 - x = 14 + 6x \][/tex]
To achieve this simplification, we combined the constant terms on the right side of the equation. Here’s the detailed process:
1. Identify the constant terms on the right side of the equation: [tex]\(5\)[/tex] and [tex]\(9\)[/tex].
2. Combine [tex]\(5\)[/tex] and [tex]\(9\)[/tex]:
[tex]\[ 5 + 9 = 14 \][/tex]
So, the right side of the equation, [tex]\(5 + 6x + 9\)[/tex], simplifies to:
[tex]\[ 14 + 6x \][/tex]
Therefore, the equation becomes:
[tex]\[ -22 - x = 14 + 6x \][/tex]
The mathematical operation used here is combining the like terms (the constant terms [tex]\(5\)[/tex] and [tex]\(9\)[/tex]). Thus, the justification for this step is:
[tex]\[ \boxed{\text{B. combining like terms}} \][/tex]
[tex]\[ -22 - x = 5 + 6x + 9 \][/tex]
Step 1 simplifies the right side of the equation:
[tex]\[ -22 - x = 14 + 6x \][/tex]
To achieve this simplification, we combined the constant terms on the right side of the equation. Here’s the detailed process:
1. Identify the constant terms on the right side of the equation: [tex]\(5\)[/tex] and [tex]\(9\)[/tex].
2. Combine [tex]\(5\)[/tex] and [tex]\(9\)[/tex]:
[tex]\[ 5 + 9 = 14 \][/tex]
So, the right side of the equation, [tex]\(5 + 6x + 9\)[/tex], simplifies to:
[tex]\[ 14 + 6x \][/tex]
Therefore, the equation becomes:
[tex]\[ -22 - x = 14 + 6x \][/tex]
The mathematical operation used here is combining the like terms (the constant terms [tex]\(5\)[/tex] and [tex]\(9\)[/tex]). Thus, the justification for this step is:
[tex]\[ \boxed{\text{B. combining like terms}} \][/tex]
