Alright, let's solve the equation step-by-step.
We start with the given equation:
[tex]\[ x + 12.7 = -25.2 \][/tex]
Next, we'll use the subtraction property of equality to isolate [tex]\( x \)[/tex]. The subtraction property of equality allows us to subtract the same amount from both sides of the equation:
[tex]\[ x + 12.7 - 12.7 = -25.2 - 12.7 \][/tex]
Now, we simplify both sides of the equation. On the left side, [tex]\( 12.7 - 12.7 \)[/tex] equals [tex]\( 0 \)[/tex], and on the right side, [tex]\(-25.2 - 12.7\)[/tex] equals [tex]\(-37.9\)[/tex]. This is achieved through the additive inverse property (where adding a number to its negative gives zero):
[tex]\[ x + 0 = -37.9 \][/tex]
Finally, using the identity property of addition, which states that adding zero to a number doesn’t change the value of the number, we have:
[tex]\[ x = -37.9 \][/tex]
Now, let's match the justifications to each statement in the solution:
1. Given:
[tex]\[
x + 12.7 = -25.2
\][/tex]
2. Subtraction property of equality:
[tex]\[
x + 12.7 - 12.7 = -25.2 - 12.7
\][/tex]
3. Additive inverse/simplification:
[tex]\[
x + 0 = -37.9
\][/tex]
4. Identity property of addition:
[tex]\[
x = -37.9
\][/tex]
Therefore, the matched justifications are:
[tex]\[
\begin{aligned}
x + 12.7 &= -25.2 \quad & \text{(given)} \\
x + 12.7 - 12.7 &= -25.2 - 12.7 \quad & \text{(subtraction property of equality)} \\
x + 0 &= -37.9 \quad & \text{(additive inverse/simplification)} \\
x &= -37.9 \quad & \text{(identity property of addition)}
\end{aligned}
\][/tex]
