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

1) How can we get Equation B from Equation A?

Choose 1 answer:
A. Multiply/divide both sides by the same non-zero constant
B. Multiply/divide only one side by a non-zero constant
C. Rewrite one side (or both) by combining like terms
D. Rewrite one side (or both) using the distributive property

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 :

GinnyAnsweridn
Let's break down the problem step-by-step:

### Part 1: How to Derive Equation B from Equation A

Given:
- Equation A: [tex]\( 3(x + 2) = 18 \)[/tex]
- Equation B: [tex]\( x + 2 = 18 \)[/tex]

We need to determine how Equation B can be derived from Equation A. Let's analyze the steps required:

1. Simplify Equation A using the distributive property:

[tex]\( 3(x + 2) = 18 \)[/tex]

Applying the distributive property:

[tex]\( 3 \cdot x + 3 \cdot 2 = 18 \)[/tex]

Which simplifies to:

[tex]\( 3x + 6 = 18 \)[/tex]

2. Isolate the variable [tex]\(x\)[/tex]:

To solve for [tex]\( x \)[/tex], we need to isolate it on one side of the equation. We'll subtract 6 from both sides:

[tex]\( 3x + 6 - 6 = 18 - 6 \)[/tex]

This simplifies to:

[tex]\( 3x = 12 \)[/tex]

Next, we divide by 3:

[tex]\( \frac{3x}{3} = \frac{12}{3} \)[/tex]

Which simplifies to:

[tex]\( x = 4 \)[/tex]

However, this process does not match Equation B. Instead, it appears that:

- Equation B is not derived from Equation A by any direct, simple algebraic manipulation.

Given the options:
- (A) Multiply/divide both sides by the same non-zero constant
- (B) Multiply/divide only one side by a non-zero constant
- (C) Rewrite one side (or both) by combining like terms
- (D) Rewrite one side (or both) using the distributive property

The correct choice is:

### Answer 1: (A) Multiply/divide both sides by the same non-zero constant

### Part 2: Are the Equations Equivalent?

To determine if the equations are equivalent, we need to check if they have the same solution set.

Solve Equation B:

Equation B: [tex]\( x + 2 = 18 \)[/tex]

Subtract 2 from both sides:

[tex]\( x = 18 - 2 \)[/tex]

Which simplifies to:

[tex]\( x = 16 \)[/tex]

Given the solutions:
- Equation A solution: [tex]\( x = 4 \)[/tex]
- Equation B solution: [tex]\( x = 16 \)[/tex]

The solutions are different, meaning the equations are not equivalent.

Given the options:
- (A) Yes
- (B) No

The correct choice is:

### Answer 2: (B) No

Thus, the complete process shows the steps leading to the answers:

1) (A) Multiply/divide both sides by the same non-zero constant

2) (B) No
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