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What is the justification for step 1 in the solution process?

[tex]\[ -22 - x = 5 + 6x + 9 \][/tex]

Step 1: [tex]\[ -22 - x = 14 + 6x \][/tex]

A. The multiplication property of equality
B. Combining like terms
C. The subtraction property of equality
D. The addition property of equality

Sagot :

GinnyAnswer
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]
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