Question

Answer two questions about Equations AAA and BBB: \begin{aligned} A.&&2x-1+3x&=0 \\\\ B.&&5x-1&=0 \end{aligned} A. B. ​ ​ 2x−1+3x 5x−1 ​ =0 =0 ​ 1) How can we get Equation BBB from Equation AAA? Choose 1 answer: Choose 1 answer: (Choice A) A Add/subtract the same quantity to/from both sides (Choice B) B Add/subtract a quantity to/from only one side (Choice C) C Rewrite one side (or both) by combining like terms (Choice D) 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: Choose 1 answer: (Choice A) A Yes (Choice B) B No

Answer 1

Answer:

1. Rewrite one side (or both) by combining like terms

2. They are equivalent

Step-by-step explanation:

Given

A. 2x-1+3x=0

B. 5x-1=0

Required

How to get equation B from A?

Are both equations equivalent?

- How to get equation B from A?

Option C answers this question

This is shown below

Equation A can be rewritten as thus:

$2x - 1 + 3x=0$

Collect Like Terms

$2x + 3x -1=0$

This gives

$5x-1=0$

At this stage, we have equation B

- Are both equations equivalent?

Yes they are:

This is shown below:

Equation A was solved in (1) above to give:

$5x-1=0$

And Equation B is

$5x-1=0$

Hence:

We can conclude that both are equivalent

Answer 2

The given equations are equivalent and this can be determined by combining like terms by using the arithmetic operations.

Given :

• 2x - 1 + 3x = 0    --- (1)

• 5x - 1 = 0   --- (2)

The following steps can be used in order to determine the correct statement:

Step 1 - Write the given equations.

2x - 1 + 3x = 0

5x - 1 = 0

Step 2 - The arithmetic operations can be used in order to determine the correct statement.

Step 3 - Add 2x and 3x in equation (1).

5x - 1 = 0   --- (3)

Step 4 - Compare both equations (3) and (2). It can be concluded that both equations are identical.

Therefore, the correct option is C).

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