Question

Which two statements are correct when simplifying this expression?

−7(9x − 5)
Responses
A First, distribute −7.First, distribute −7.
B First, calculate −7 + (−5).First, calculate −7 + (−5).
C −7(9x −5) = −63x − 35.−7(9x −5) = −63x − 35.
D −7(9x −5) = −63x + 35.−7(9x −5) = −63x + 35.
E −7(9x −5) = 63x − 35.−7(9x −5) = 63x − 35.

Answer 1

To simplify the expression \( -7(9x - 5) \), we need to distribute \(-7\) to both terms inside the parentheses:

1. Distribute \(-7\) to \(9x\):
\[
-7 \cdot 9x = -63x
\]

2. Distribute \(-7\) to \(-5\):
\[
-7 \cdot -5 = +35
\]

Putting it together, we get:
\[
-7(9x - 5) = -63x + 35
\]

Now let's evaluate the provided statements:

A. First, distribute −7.
**Correct:** This is the first step to simplify the expression.

B. First, calculate −7 + (−5).
**Incorrect:** This does not represent a valid step in simplifying the expression.

C. −7(9x − 5) = −63x − 35.
**Incorrect:** The sign in front of the \(35\) is wrong; it should be \(+35\).

D. −7(9x − 5) = −63x + 35.
**Correct:** This is accurate based on our simplification.

E. −7(9x − 5) = 63x − 35.
**Incorrect:** Both the coefficient of \(x\) and the constant term have incorrect signs.

Thus, the correct statements are **A** and **D**.

Answer 2

Simplify (3x − 8) + (2x + 5) − (4x − 8).
Responses
A x − 11x − 11
B x + 5x + 5
C x + 21x + 21
D 9x + 59x + 5
E 9x − 119x − 11

Answer 3

To simplify the expression \((3x - 8) + (2x + 5) - (4x - 8)\), follow these steps:

1. Expand the expression:
- \((3x - 8) + (2x + 5) - (4x - 8)\)
- Distributing the negative sign to \( (4x - 8) \) gives us:
- \( (3x - 8) + (2x + 5) - 4x + 8 \)

2. Combine like terms:
- Combine the \(x\) terms: \(3x + 2x - 4x = 1x\) or simply \(x\)
- Combine the constant terms: \(-8 + 5 + 8 = -8 + 5 + 8 = 5\)

Putting it all together, we have:
\[
(3x - 8) + (2x + 5) - (4x - 8) = x + 5
\]

Now, let's evaluate the provided responses:

A. \(x - 11\)
**Incorrect**

B. \(x + 5\)
**Correct**

C. \(x + 21\)
**Incorrect**

D. \(9x + 5\)
**Incorrect**

E. \(9x - 11\)
**Incorrect**

The correct answer is **B**: \(x + 5\).

Answer 4

Which two statements are correct when simplifying this expression?

12 + 6(3x − 2)
Responses
A First, calculate 6(3x − 2)First, calculate 6(3x − 2)
B First, calculate 12 + 6.First, calculate 12 + 6.
C 12 + 6(3x − 2) = 54x − 3612 + 6(3x − 2) = 54x − 36
D 12 + 6(3x − 2) = 18x12 + 6(3x − 2) = 18x
E 12 + 6(3x − 2) = 18x − 24

Answer 5

To simplify the expression \(12 + 6(3x - 2)\), we should follow these steps:

1. **Distribute** \(6\) to both terms inside the parentheses:
\[
6(3x) - 6(2) = 18x - 12
\]

2. Now, combine this with the \(12\) from the original expression:
\[
12 + (18x - 12) = 18x + 0 = 18x
\]

Now let's evaluate the provided statements based on this simplification:

A. **First, calculate \(6(3x - 2)\)**
**Correct:** This is the first step in simplifying the expression.

B. **First, calculate \(12 + 6\)**
**Incorrect:** This does not represent a valid step in simplifying the expression.

C. **\(12 + 6(3x - 2) = 54x - 36\)**
**Incorrect:** This is incorrect based on our calculation; the coefficients and constants do not match.

D. **\(12 + 6(3x - 2) = 18x\)**
**Correct:** This is the correct simplification of the expression.

E. **\(12 + 6(3x - 2) = 18x - 24\)**
**Incorrect:** This is incorrect since the constant term is not accurate based on the simplification we performed.

The two correct statements are **A** and **D**.

Answer 6

Which expression is equivalent to the following expression: – 1 (10x + 15) – 2 ?
5
Responses
A -2x – 1 -2 x – 1
B -2x – 4-2 x – 4
C -2x – 3-2 x – 3
D -2x – 5

Answer 7

To simplify the expression \(-\frac{1}{5}(10x + 15) - 2\), follow these steps:

1. **Distribute \(-\frac{1}{5}\)** to both terms in the parentheses:
\[
-\frac{1}{5} \cdot 10x - \frac{1}{5} \cdot 15 = -2x - 3
\]

2. Now, combine this with the \(-2\) from the original expression:
\[
-2x - 3 - 2 = -2x - 5
\]

So the entire expression simplifies to:
\[
-2x - 5
\]

Now let's evaluate the provided responses:

A. \(-2x - 1\)
**Incorrect**

B. \(-2x - 4\)
**Incorrect**

C. \(-2x - 3\)
**Incorrect**

D. \(-2x - 5\)
**Correct**

Thus, the equivalent expression is **D**: \(-2x - 5\).

Answer 8

Given:



(10x − 10y) −

(12x − 24y)

Which of the following expressions is equivalent to the given expression?

Responses
A −5x + 14y−5x + 14y
B −5x − 14y−5x − 14y
C 5x + 14y5x + 14y
D 5x − 14y

Answer 9

To simplify the expression \((10x - 10y) - (12x - 24y)\), follow these steps:

1. **Distribute the negative sign** to the second expression:
\[
(10x - 10y) - (12x - 24y) = (10x - 10y) - 12x + 24y
\]

2. **Combine like terms**:
- Combine the \(x\) terms:
\[
10x - 12x = -2x
\]
- Combine the \(y\) terms:
\[
-10y + 24y = 14y
\]

Now, putting it all together, we have:
\[
-2x + 14y
\]

Now, let's check the provided answers to see which one is equivalent to \(-2x + 14y\):

A. \(-5x + 14y\)
**Incorrect**

B. \(-5x - 14y\)
**Incorrect**

C. \(5x + 14y\)
**Incorrect**

D. \(5x - 14y\)
**Incorrect**

None of the provided responses directly match the simplified expression \(-2x + 14y\).

Let's double-check:

- Original expression: \((10x - 10y) - (12x - 24y)\)
- Simplified to: \(-2x + 14y\)

It appears none of the provided options are correct equivalents for the given expression. Would you like to recheck the options or is there anything else I can assist you with?

Answer 10

Which expression is equivalent to -3(2y – 5)?
Responses
A -6y - 15-6 y - 15
B -6y + 15-6 y + 15
C -6y + 5-6 y + 5
D -6y - 8

Answer 11

To simplify the expression \(-3(2y - 5)\), follow these steps:

1. **Distribute \(-3\)** to both terms inside the parentheses:
\[
-3 \cdot 2y + (-3) \cdot (-5) = -6y + 15
\]

Putting it all together, we have:
\[
-3(2y - 5) = -6y + 15
\]

Now let's evaluate the provided responses:

A. \(-6y - 15\)
**Incorrect**

B. \(-6y + 15\)
**Correct**

C. \(-6y + 5\)
**Incorrect**

D. \(-6y - 8\)
**Incorrect**

The correct answer is **B**: \(-6y + 15\).