Answer :
Let's examine the two questions step by step:
### Question 1: How can we get Equation [tex]\( B \)[/tex] from Equation [tex]\( A \)[/tex]?
We'll start with Equation [tex]\( A \)[/tex]:
[tex]\[ 3(x + 2) = 18 \][/tex]
To transform Equation [tex]\( A \)[/tex] into Equation [tex]\( B \)[/tex], we need to isolate [tex]\( x + 2 \)[/tex]. We can do this by dividing both sides of Equation [tex]\( A \)[/tex] by the same non-zero constant, which is 3 in this case.
Here's the detailed process:
1. Start with the given Equation [tex]\( A \)[/tex]:
[tex]\[ 3(x + 2) = 18 \][/tex]
2. Divide both sides of the equation by 3:
[tex]\[ \frac{3(x + 2)}{3} = \frac{18}{3} \][/tex]
3. Simplify the left side and the right side:
[tex]\[ x + 2 = 6 \][/tex]
This results in Equation [tex]\( B \)[/tex]:
[tex]\[ x + 2 = 6 \][/tex]
Therefore, the correct answer is:
(C) Multiply/divide both sides by the same non-zero constant.
### Question 2: Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
To determine if the equations are equivalent, we can solve Equation [tex]\( A \)[/tex] and Equation [tex]\( B \)[/tex] and check if they yield the same solution.
For Equation [tex]\( B \)[/tex]:
[tex]\[ x + 2 = 6 \][/tex]
Subtract 2 from both sides:
[tex]\[ x = 4 \][/tex]
For Equation [tex]\( A \)[/tex]:
[tex]\[ 3(x + 2) = 18 \][/tex]
Divide both sides by 3 to simplify:
[tex]\[ x + 2 = 6 \][/tex]
Then, subtract 2 from both sides:
[tex]\[ x = 4 \][/tex]
Since both equations have the same solution, we can conclude that the equations are indeed equivalent.
Therefore, the correct answer is:
(A) Yes
In summary:
1. The method to get Equation [tex]\( B \)[/tex] from Equation [tex]\( A \)[/tex] is (C) Multiply/divide both sides by the same non-zero constant.
2. Based on this method, the equations are equivalent, so the answer is (A) Yes.
### Question 1: How can we get Equation [tex]\( B \)[/tex] from Equation [tex]\( A \)[/tex]?
We'll start with Equation [tex]\( A \)[/tex]:
[tex]\[ 3(x + 2) = 18 \][/tex]
To transform Equation [tex]\( A \)[/tex] into Equation [tex]\( B \)[/tex], we need to isolate [tex]\( x + 2 \)[/tex]. We can do this by dividing both sides of Equation [tex]\( A \)[/tex] by the same non-zero constant, which is 3 in this case.
Here's the detailed process:
1. Start with the given Equation [tex]\( A \)[/tex]:
[tex]\[ 3(x + 2) = 18 \][/tex]
2. Divide both sides of the equation by 3:
[tex]\[ \frac{3(x + 2)}{3} = \frac{18}{3} \][/tex]
3. Simplify the left side and the right side:
[tex]\[ x + 2 = 6 \][/tex]
This results in Equation [tex]\( B \)[/tex]:
[tex]\[ x + 2 = 6 \][/tex]
Therefore, the correct answer is:
(C) Multiply/divide both sides by the same non-zero constant.
### Question 2: Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
To determine if the equations are equivalent, we can solve Equation [tex]\( A \)[/tex] and Equation [tex]\( B \)[/tex] and check if they yield the same solution.
For Equation [tex]\( B \)[/tex]:
[tex]\[ x + 2 = 6 \][/tex]
Subtract 2 from both sides:
[tex]\[ x = 4 \][/tex]
For Equation [tex]\( A \)[/tex]:
[tex]\[ 3(x + 2) = 18 \][/tex]
Divide both sides by 3 to simplify:
[tex]\[ x + 2 = 6 \][/tex]
Then, subtract 2 from both sides:
[tex]\[ x = 4 \][/tex]
Since both equations have the same solution, we can conclude that the equations are indeed equivalent.
Therefore, the correct answer is:
(A) Yes
In summary:
1. The method to get Equation [tex]\( B \)[/tex] from Equation [tex]\( A \)[/tex] is (C) Multiply/divide both sides by the same non-zero constant.
2. Based on this method, the equations are equivalent, so the answer is (A) Yes.
