Get the best answers to your questions with the help of IDNLearn.com's experts. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.

Answer two questions about Equations [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:

[tex]\[ A. \quad 3x - 1 = 7 \][/tex]
[tex]\[ B. \quad 3x = 8 \][/tex]

1. How can we get Equation [tex]\( B \)[/tex] from Equation [tex]\( A \)[/tex]?

Choose 1 answer:
A. Multiply/divide both sides by the same non-zero constant
B. Multiply/divide both sides by the same variable expression
C. Add/subtract the same quantity to/from both sides
D. Add/subtract a quantity to/from only one side


Sagot :

Absolutely! Let's carefully analyze how we can transform Equation [tex]\(A\)[/tex] into Equation [tex]\(B\)[/tex].

Given equations:
- Equation [tex]\(A\)[/tex]: [tex]\(3x - 1 = 7\)[/tex]
- Equation [tex]\(B\)[/tex]: [tex]\(3x = 8\)[/tex]

Steps to transform Equation [tex]\(A\)[/tex] to Equation [tex]\(B\)[/tex]:

1. Starting with Equation [tex]\(A\)[/tex]:
[tex]\[ 3x - 1 = 7 \][/tex]

2. Isolate the term involving [tex]\(x\)[/tex]:
- To eliminate the [tex]\(-1\)[/tex] on the left side, we need to add [tex]\(1\)[/tex] to both sides of the equation.
- Adding [tex]\(1\)[/tex] to both sides:
[tex]\[ 3x - 1 + 1 = 7 + 1 \][/tex]
- Simplify both sides:
[tex]\[ 3x = 8 \][/tex]

3. Resulting Equation:
[tex]\[ 3x = 8 \][/tex]
- As you can see, this matches Equation [tex]\(B\)[/tex].

Conclusion:
- The transformation involves adding [tex]\(1\)[/tex] to both sides of Equation [tex]\(A\)[/tex] to achieve Equation [tex]\(B\)[/tex].

Correct Answer:
[tex]\[ \text{(C) Add/subtract the same quantity to/from both sides} \][/tex]