To match the justification to each statement in the solution of the equation [tex]\(x + 12.7 = -25.2\)[/tex], let's go through the solution step-by-step and identify the mathematical properties used:
1. Statement: [tex]\(x + 12.7 = -25.2\)[/tex]
Justification: given
The equation [tex]\(x + 12.7 = -25.2\)[/tex] is provided as the starting point. We don't need to perform any calculation here; it is simply given.
2. Statement: [tex]\(x + 12.7 - 12.7 = -25.2 - 12.7\)[/tex]
Justification: subtraction property of equality
To isolate [tex]\(x\)[/tex], we subtract 12.7 from both sides of the equation. This is based on the subtraction property of equality, which states that if you subtract the same amount from both sides of an equation, the equality is maintained.
3. Statement: [tex]\(x + 0 = -37.9\)[/tex]
Justification: additive inverse/simplification
Subtracting 12.7 from [tex]\(x + 12.7\)[/tex] leaves us with [tex]\(x + 0\)[/tex] (since [tex]\(12.7 - 12.7 = 0\)[/tex]). On the right side, [tex]\(-25.2 - 12.7\)[/tex] simplifies to [tex]\(-37.9\)[/tex]. This involves the additive inverse and simplification steps.
4. Statement: [tex]\(x = -37.9\)[/tex]
Justification: identity property of addition
Since [tex]\(x + 0\)[/tex] equals [tex]\(x\)[/tex] by the identity property of addition (which states that any number plus zero is that number itself), we simply state that [tex]\(x = -37.9\)[/tex].
Based on the logical, step-by-step solution and justifications described above, the matched solutions are:
1. [tex]\(x + 12.7 = -25.2 \quad \rightarrow \quad \text{given}\)[/tex]
2. [tex]\(x + 12.7 - 12.7 = -25.2 - 12.7 \quad \rightarrow \quad \text{subtraction property of equality}\)[/tex]
3. [tex]\(x + 0 = -37.9 \quad \rightarrow \quad \text{additive inverse/simplification}\)[/tex]
4. [tex]\(x = -37.9 \quad \rightarrow \quad \text{identity property of addition}\)[/tex]
