Simplify the expression: (2x + 2) − (3x + 11) =

Question

(1 point)
Responses

5x − 9
5x − 9

−5x − 13
−5x − 13

−x − 13
−x − 13

−x − 9

Answer 1

To simplify the expression \( (2x + 2) - (3x + 11) \), we first distribute the negative sign in front of the second parentheses:

\[ (2x + 2) - (3x + 11) = 2x + 2 - 3x - 11 \]

Next, we combine like terms. For the \(x\) terms, we have:

\[ 2x - 3x = -x \]

And for the constant terms, we have:

\[ 2 - 11 = -9 \]

Putting it all together, we get:

\[ -x - 9 \]

So the simplified expression is:

\[ -x - 9 \]

Therefore, the correct answer is:

−x − 9

Answer 2

Simplify the expression: 6(3x−5)+2(3x−5)−8(3x−5)
(1 point)
Responses

24x−40
24 x minus 40

35x−60
35 x minus 60

48x−80
48 x minus 80

0

Answer 3

To simplify the expression \( 6(3x - 5) + 2(3x - 5) - 8(3x - 5) \), we notice that all terms have a common factor of \( (3x - 5) \). We can factor that out:

\[ = (3x - 5)(6 + 2 - 8) \]

Now, we simplify the expression inside the parentheses:

\[ 6 + 2 - 8 = 8 - 8 = 0 \]

So, we have:

\[ (3x - 5)(0) = 0 \]

Therefore, the simplified expression is:

\[ 0 \]

So the correct answer is:

0

Answer 4

Evaluate the expression −4x+7y
when x=−2
and y=−4
.(1 point)
Responses

−20
negative 20

36
36

−36
negative 36

20

Answer 5

To evaluate the expression \( -4x + 7y \) when \( x = -2 \) and \( y = -4 \), we plug in the values of \( x \) and \( y \):

\[ -4(-2) + 7(-4) \]

Calculating each part:

1. Calculate \( -4(-2) \): \[ -4 \times -2 = 8 \]

2. Calculate \( 7(-4) \): \[ 7 \times -4 = -28 \]

Now combine the results:

\[ 8 + (-28) = 8 - 28 = -20 \]

Thus, the value of the expression \( -4x + 7y \) when \( x = -2 \) and \( y = -4 \) is:

\[ -20 \]

Therefore, the correct answer is:

−20

Answer 6

Simplify 4x+6(3x−2)
(1 point)
Responses

18x−2
18 x minus 2

22x−12
22 x minus 12

22x−2
22 x minus 2

10x−12

Answer 7

To simplify the expression \( 4x + 6(3x - 2) \), we start by distributing the \(6\) into the parentheses:

\[ 6(3x - 2) = 6 \cdot 3x - 6 \cdot 2 = 18x - 12 \]

Now, we can rewrite the original expression:

\[ 4x + 6(3x - 2) = 4x + (18x - 12) \]

Next, we combine like terms:

\[ 4x + 18x - 12 = (4x + 18x) - 12 = 22x - 12 \]

Thus, the simplified expression is:

\[ 22x - 12 \]

Therefore, the correct answer is:

22x − 12

Answer 8

Simplify 1/3(9x − 5)
(1 point)
Responses

3x−5
3 x minus 5

6x−5
6 x minus 5

6x−2
6 x minus 2

3x−5/3

Answer 9

To simplify the expression \(\frac{1}{3}(9x - 5)\), we distribute \(\frac{1}{3}\) to each term inside the parentheses:

\[ \frac{1}{3} \cdot 9x - \frac{1}{3} \cdot 5 \]

Calculating each term:

1. \(\frac{1}{3} \cdot 9x = 3x\)
2. \(\frac{1}{3} \cdot 5 = \frac{5}{3}\)

So we can rewrite the expression as:

\[ 3x - \frac{5}{3} \]

Therefore, the simplified expression is:

\[ 3x - \frac{5}{3} \]

Thus, the correct choice is:

3x − 5/3

Answer 10

Which factorization is equivalent to this expression?

30x+70


(1 point)
Responses

10(x+7)
10 times open paren x plus 7 close paren

30(x+2)
30 times open paren x plus 2 close paren

7(3x+10)
7 times open paren 3 x plus 10 close paren

10(3x+7)

Answer 11

To determine which factorization is equivalent to the expression \(30x + 70\), we can first factor out the greatest common factor (GCF) from the expression.

The GCF of \(30x\) and \(70\) is \(10\). So, we can factor out \(10\):

\[ 30x + 70 = 10(3x + 7) \]

Now, let's compare with the provided choices:

1. \(10(x + 7)\)
2. \(30(x + 2)\)
3. \(7(3x + 10)\)
4. \(10(3x + 7)\)

From the factorization we derived, we can see that:

10(3x + 7) is the correct factorization that is equivalent to \(30x + 70\).

Thus, the correct answer is:

10(3x + 7).