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Answer two questions about Equations [tex]$A$[/tex] and [tex]$B$[/tex]:

A. [tex]$3(x+2)=18$[/tex]
B. [tex]$x+2=6$[/tex]

1) How can we get Equation [tex]$B$[/tex] from Equation [tex]$A$[/tex]?

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

2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?

Choose 1 answer:
A. Yes
B. No

Sagot :

GinnyAnswer
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.
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