Which expression is equivalent to -4(y – 7)?

Question

Responses.
A -4y - 28-4 y - 28
B -4y - 7-4 y - 7
C -4y - 11-4 y - 11
D -4y + 28

Answer 1

To simplify the expression \(-4(y - 7)\), you can apply the distributive property:

\[ -4(y - 7) = -4 \cdot y + (-4) \cdot (-7) \]

This simplifies to:

\[ -4y + 28 \]

Thus, the expression is equivalent to:

\[ -4y + 28 \]

Looking at the choices provided, the correct response is:

D \(-4y + 28\)

Answer 2

Which expression is equivalent to 2(2x + 7)?
Responses
A 4x - 144 x - 14
B 4x + 144 x + 14
C 14x + 414 x + 4
D 8x + 14

Answer 3

To simplify the expression \(2(2x + 7)\), we can apply the distributive property:

\[ 2(2x + 7) = 2 \cdot 2x + 2 \cdot 7 \]

This simplifies to:

\[ 4x + 14 \]

Looking at the choices provided, the expression equivalent to \(2(2x + 7)\) is:

B \(4x + 14\)

Answer 4

Which expression is equivalent to −3x + 5.1?
Responses
A −3(x + 1.7)−3(x + 1.7)
B −3(x − 1.7)−3(x − 1.7)
C 3(x + 1.7)3(x + 1.7)
D 3(x − 1.7)

Answer 5

To determine which expression is equivalent to \(-3x + 5.1\), we need to manipulate each option and see if it can be simplified to \(-3x + 5.1\).

A. \(-3(x + 1.7)\)
Using distribution:
\(-3(x + 1.7) = -3x - 5.1\) (not equivalent)

B. \(-3(x - 1.7)\)
Using distribution:
\(-3(x - 1.7) = -3x + 5.1\) (equivalent)

C. \(3(x + 1.7)\)
Using distribution:
\(3(x + 1.7) = 3x + 5.1\) (not equivalent)

D. \(3(x - 1.7)\)
Using distribution:
\(3(x - 1.7) = 3x - 5.1\) (not equivalent)

The only option that is equivalent to \(-3x + 5.1\) is:

B \(-3(x - 1.7)\)

Answer 6

Simplify: -0.8b + 4.1c - (-3.2b) - 0.1c
Responses
A -2.4b + 4c-2.4b + 4c
B 2.4b + 4c2.4b + 4c
C 2.4c + 4b2.4c + 4b
D 2.4b - 4c

Answer 7

Let's simplify the expression step by step:

We start with: \[ -0.8b + 4.1c - (-3.2b) - 0.1c \]

First, simplify the double negative: \[ -0.8b + 4.1c + 3.2b - 0.1c \]

Next, combine the like terms for \(b\) and \(c\):

1. For \(b\): \[ -0.8b + 3.2b = (3.2 - 0.8)b = 2.4b \]

2. For \(c\): \[ 4.1c - 0.1c = (4.1 - 0.1)c = 4.0c \]

Putting it all together, we have: \[ 2.4b + 4c \]

So the simplified expression is: \[ 2.4b + 4c \]

The correct answer is: B \(2.4b + 4c\)

Answer 8

Which expression is equivalent to the following expression: – 1/5 (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 9

To simplify the expression \(-\frac{1}{5}(10x + 15) - 2\), we first apply the distributive property:

\[ -\frac{1}{5}(10x + 15) = -\frac{1}{5} \cdot 10x - \frac{1}{5} \cdot 15 \]

Calculating each term gives:

\[ -\frac{10}{5}x - \frac{15}{5} = -2x - 3 \]

So now, we include the \(-2\):

\[ -2x - 3 - 2 \]

Simplifying this results in:

\[ -2x - 5 \]

Thus, the final simplified expression is:

\[ -2x - 5 \]

The correct response is:

D \(-2x - 5\)

Answer 10

An expression is shown. - 3/4 (24x - 12) = ____ + ____
Put responses in the correct input to answer the question.
Response area
18z
-21x
-18x
-32x
-16
-9
9
16

Move a term into each blank to create an equivalent expression.

Answer 11

To simplify the expression \(-\frac{3}{4}(24x - 12)\), we can apply the distributive property:

\[ -\frac{3}{4}(24x - 12) = -\frac{3}{4} \cdot 24x + -\frac{3}{4} \cdot (-12) \]

Now, let's calculate each term:

1. For the first term: \[ -\frac{3}{4} \cdot 24x = -18x \]

2. For the second term: \[ -\frac{3}{4} \cdot (-12) = 9 \]

Putting these together gives us: \[ -\frac{3}{4}(24x - 12) = -18x + 9 \]

So, we can fill in the blanks as follows:

• The first blank will be -18x
• The second blank will be 9

Thus, the final expression would be: \(-\frac{3}{4}(24x - 12) = -18x + 9\)