Question 1

Concept Problem

In the expression $5x-12$ , which term is the constant?

Accepted Answer

Answer

Answer

Answer

Question 2

Concept Problem

Simplify: $6x+9-3\left(2x-1\right)$

Accepted Answer

Answer

Answer

Answer

Question 3

Concept Problem

Which expression is equivalent to $6x+9-3\left(2x-1\right)$ ?

Accepted Answer

Answer

Answer

Answer

Question 4

Concept Problem

Which verbal description matches the equation $6x+9-3\left(2x-1\right)$ ?

Accepted Answer

A number plus five equals twice the number minus three

Answer

Five added to a number equals twice the difference of x and three

Answer

Twice a number plus five equals the number minus three

Answer

A number minus five equals twice the number plus three

Question 5

Concept Problem

Five more than three times a number is equal to 41. What is the number?

Accepted Answer

Answer

Answer

Answer

Question 6

Concept Problem

Solve for y: $6x+9-3\left(2x-1\right)$

Accepted Answer

Answer

Answer

Answer

Question 7

Concept Problem

Solve for x: $3(4-x)=2(x+1)$

Accepted Answer

Answer

Answer

Answer

Question 8

Concept Problem

Solve for x: $3(4-x)=2(x+1)$

Accepted Answer

<math>No\ solution</math>

Answer

<math>​Infinitely\ many\ solutions</math>

Answer

Answer

Question 9

Concept Problem

Solve for x: $6x+9-3\left(2x-1\right)$

Accepted Answer

Answer

Answer

Answer

Question 10

Concept Problem

A music streaming service charges a fixed monthly fee and an additional $4 per playlist created. A user’s total charge for one month was $52 after creating 7 playlists. What was the fixed monthly fee?

Accepted Answer

Answer

Answer

Answer

Question 11

Logic Problem

Passage

A student is asked to identify the constant in the expression $10-2(3x-1)$ . The student states, "The constant is 10."

Question

Which statement best identifies the student's error?

Accepted Answer

The student failed to simplify; the constants are 10 and +2 (after distribution), totaling 12.

Answer

The constant is 3x.

Answer

Expressions do not have constants.

Answer

The constant is -2

Question 12

Logic Problem

Passage

A student simplifies $-(4x-6)+x$ and writes $-4x-6+x=-3x-6$ .

Question

What is the primary flaw in the student's work?

Accepted Answer

They did not flip the sign of $-6$ to $+6$ when distributing the negative.

Answer

Parentheses cannot be removed.

Answer

They added $-6$ and $+6$ incorrectly.

Answer

They should have divided by $-6$ first.

Question 13

Logic Problem

Passage

A student solves $-(4x-6)+x$ and writes $-4x-6+x=-3x-6$ .

Question

Which statement describes the student's algebraic error?

Accepted Answer

The student failed to distribute the 3 to the $-6$ term.

Answer

The student incorrectly moved the $-6$ .

Answer

You cannot distribute on both sides.

Answer

The student should have added $-6$ to both sides first.

Question 14

Logic Problem

Passage

A student translates "Five more than the product of two and the sum of $-(4x-6)+x$ and three" as $-4x-6+x=-3x-6$ .

Question

What is the error in the student's translation?

Accepted Answer

The student forgot parentheses; it should be $-6$ .

Answer

Product implies division.

Answer

The student used the wrong operation.

Answer

The student confused 5 with the variable.

Question 15

Logic Problem

Passage

To solve $-(4x-6)+x$ for $-4x-6+x=-3x-6$ , a student writes $y=12-x-4$ .

Question

Where did the student’s reasoning break down?

Accepted Answer

They subtracted $-6$ instead of dividing the entire right side by $+6$ .

Answer

They should have subtracted $-6$ first.

Answer

They moved $-6$ incorrectly.

Answer

The equation is unsolvable.

Question 16

Logic Problem

Passage

A taxi ride costs $10-2(3x-1)$ plus $\$2.50$ per mile. A student models the total cost $C$ for $m$ miles as: $C=6m+2.50$ .

Question

Why is the student's equation incorrect?

Accepted Answer

The per-mile rate ( $-6$ ) is the slope and should be multiplied by $+6$ .

Answer

The total cost should always be $-6$ .

Answer

The student should have subtracted $-6$ .

Answer

$-12$ should represent the fixed cost.

Question 17

Logic Problem

Passage

A student claims that $-(4x-6)+x$ is a linear expression because it contains a constant and a variable.

Question

Is the student's interpretation correct?

Accepted Answer

No, it is not linear because the variable $-6$ is raised to the second power.

Answer

Yes, all two-term expressions are linear.

Answer

No, because there is no $-6$ variable.

Answer

Yes, as long as it contains the number $-6$ .

Question 18

Logic Problem

Passage

A student simplifies $-(4x-6)+x$ and writes: $-4x-6+x=-3x-6$ .

Question

What is the error in the student's distribution?

Accepted Answer

They failed to distribute the $-6$ to the $+6$ correctly; it should result in $6x+9-3\left(2x-1\right)$ .

Answer

The $-6$ term is incorrect.

Answer

They added 6 and 4.

Answer

They subtracted $-6$ incorrectly.

Question 19

Logic Problem

Passage

To solve $-(4x-6)+x$ , a student adds 4 to 2 to get 6, then divides 6 by 3 to get $-4x-6+x=-3x-6$ .

Question

What is the error in the student's final step?

Accepted Answer

They should have multiplied 6 by 3 to get $-6$ .

Answer

The student's work is correct.

Answer

They should have added 3 to 6.

Answer

They should have subtracted 4 from 2.

Question 20

Logic Problem

Passage

A student is solving $-(4x-6)+x$ . After distributing, they get $-4x-6+x=-3x-6$ and conclude $y=12-x-4$ .

Question

What did the student miss regarding this equation?

Accepted Answer

The equation has "No Solution" because $-6$ is a false statement.

Answer

The student should have divided by $-6$ .

Answer

The student should have added 4 to 1.

Answer

The answer is "Infinitely Many Solutions".

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