Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
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!
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!
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
