Question at position 3

Question

3

Multiple Choice
3 points



Question at position 3

The following is a student's work for solving the equation 5x + 1 = 5x + 4



What the student did:

Their work:

1. Rewrite the equation

→ image.png


2. Get rid of the variable on the right side of the equation by using the inverse operation.



→ image.png

3. Combine like terms
(the 5x and -5x will result in 0 for both sides).

→ 0 + 1 = 0 + 4

4. Simplify both sides.

→ 1 = 4


Based on step 4, what we can conclude (select all that applies)?

The following is a student's work for solving the equation 5x + 1 = 5x + 4



What the student did:

Their work:

1. Rewrite the equation

→ image.png


2. Get rid of the variable on the right side of the equation by using the inverse operation.



→ image.png

3. Combine like terms
(the 5x and -5x will result in 0 for both sides).

→ 0 + 1 = 0 + 4

4. Simplify both sides.

→ 1 = 4


Based on step 4, what we can conclude (select all that applies)?

This equation has no solution.

This equation has one solution.

This equation has infinitely many solutions.

Question at position 4
4

Multiple Choice
3 points



Question at position 4

The following is a student's work for solving the equation 3(x + 1) = 3x + 4 - 1



What the student did:

Their work:

1. Rewrite the equation

→ image.png


2. Apply the distributive property on the left side.



→ image.png

3. Combine like terms on both sides
(only the right side contains like terms).

→ image.png

4. The left side is identical to the right side.

→ image.png


Based on step 4, what we can conclude (select all that applies)?

The following is a student's work for solving the equation 3(x + 1) = 3x + 4 - 1



What the student did:

Their work:

1. Rewrite the equation

→ image.png


2. Apply the distributive property on the left side.



→ image.png

3. Combine like terms on both sides
(only the right side contains like terms).

→ image.png

4. The left side is identical to the right side.

→ image.png


Based on step 4, what we can conclude (select all that applies)?

This equation has no solution.

This equation has one solution.

Answer 1

For Question 3 regarding the equation \( 5x + 1 = 5x + 4 \):

1. The student's final simplification results in \( 1 = 4 \), which is a false statement.
2. Since the student arrived at a contradiction (a false statement), we can conclude that the original equation has no solutions.

Therefore, the correct conclusion is:

• This equation has no solution.

For Question 4 regarding the equation \( 3(x + 1) = 3x + 4 - 1 \):

1. The statement that the left side is identical to the right side implies that the two expressions are equal for all values of \( x \).
2. When two expressions are identical for all values of \( x \), it indicates that there are infinitely many solutions.

Therefore, the correct conclusion is:

• This equation has infinitely many solutions.

In summary:

• For Question 3: "This equation has no solution."
• For Question 4: "This equation has infinitely many solutions."