At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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 :

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.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.