Certainly! Let's solve the one-step equation [tex]\( x + 12.7 = -25.2 \)[/tex] step-by-step and match each step with its appropriate justification.
1. Start with the given equation:
[tex]\[ x + 12.7 = -25.2 \][/tex]
- Justification: This equation is provided to us exactly as it is.
- Label: Given
- [tex]\( \boxed{\text{given}} \)[/tex]
2. Apply the subtraction property of equality:
[tex]\[ x + 12.7 - 12.7 = -25.2 - 12.7 \][/tex]
- Justification: To isolate [tex]\( x \)[/tex], we subtract 12.7 from both sides of the equation. This step uses the subtraction property of equality which states that if you subtract the same number from both sides of an equation, the equality is maintained.
- Label: Subtraction property of equality
- [tex]\( \boxed{\text{subtraction property of equality}} \)[/tex]
3. Simplify the equation:
[tex]\[ x = -37.9 \][/tex]
- Justification: Simplifying both sides of the equation by performing the subtraction. [tex]\( x + 0 = x \)[/tex] and [tex]\(-25.2 - 12.7 = -37.9\)[/tex].
- Label: Additive inverse/simplification
- [tex]\( \boxed{\text{additive inverse/simplification}} \)[/tex]
4. Using the identity property of addition:
[tex]\[ x + 0 = -37.9 \][/tex]
- Justification: In this step, recognizing that [tex]\( x + 0 \)[/tex] is simply [tex]\( x \)[/tex] illustrates the identity property of addition. This property states that any number plus zero is the number itself.
- Label: Identity property of addition
- [tex]\( \boxed{\text{identity property of addition}} \)[/tex]
Now, we match each statement with its corresponding justification:
[tex]\[
\begin{aligned}
&x + 12.7 = -25.2 &\rightarrow \boxed{\text{given}}\\
&x + 12.7 - 12.7 = -25.2 - 12.7 &\rightarrow \boxed{\text{subtraction property of equality}}\\
&x = -37.9 &\rightarrow \boxed{\text{additive inverse/simplification}}\\
&x + 0 = -37.9 &\rightarrow \boxed{\text{identity property of addition}}
\end{aligned}
\][/tex]
And there you have the complete step-by-step solution with each statement appropriately justified!
