Question

Simplify 4x + 8x using the properties of operations.(1 point)
Responses.

12x
12 x

4 + 8x
4 plus 8 x

12x^2
12 x squared

4x + 8

Answer 1

Simplify 9g−7h−6g + 2h . (1 point)
Responses

−2gh
negative 2 g h

3g + 5h
3 g plus 5 h

3g − 5h
3 g minus 5 h

2gh − 4gh

Answer 2

Simplify 2a − 4b +7 + 8a + 6b − 2 .(1 point)
Responses

10a + 2b +5
10 a plus 2 b plus 5

10a − 2b +5
10 a minus 2 b plus 5

12ab + 5
12 a b plus 5

−2ab + 14ab + 5

Answer 3

Simplify 3/7x + 2/7x using properties of operations.(1 point)
Responses

5/7x
Start Fraction 5 over 7 End Fraction x

5/7x^2
Start Fraction 5 over 7 End Fraction x squared

5/14x^2
Start Fraction 5 over 14 End Fraction x squared

5/14^x

Answer 4

Simplify 6/7c − 5/9d − 1/2 c + 1/3d .(1 point)
Responses

5/9c + 4/12d = 5/9c +1/3d
Start Fraction 5 over 9 End Fraction c plus Start Fraction 4 over 1/2 End Fraction d equals Start Fraction 5 over 9 End Fraction c plus Start Fraction 1 over 3 End Fraction d

5/14c − 2/9d
Start Fraction 5 over 14 End Fraction c minus Start Fraction 2 over 9 End Fraction d

5/14c + 2/9d
Start Fraction 5 over 14 End Fraction c plus Start Fraction 2 over 9 End Fraction d

5/9c − 4/12d = 5/9c −1/3d

Answer 5

Expand 5(y + 2) using the distributive property.(1 point)
Responses

6y + 10
6 y plus 10

5y + 10
5 y plus 10

5y + 2
5 y plus 2

6y + 7

Answer 6

To simplify \(4x + 8x\), you can combine the like terms.

Here are the steps:

1. Identify the like terms: \(4x\) and \(8x\).
2. Add the coefficients: \(4 + 8 = 12\).
3. Keep the variable \(x\).

So, \(4x + 8x = 12x\).

The correct response is:

**12x**

Answer 7

To simplify the expression \(9g - 7h - 6g + 2h\), follow these steps:

1. Combine the \(g\) terms: \(9g - 6g = 3g\).
2. Combine the \(h\) terms: \(-7h + 2h = -5h\).

Putting it all together, you get:

\[3g - 5h\]

So the correct response is:

**3g − 5h**

Answer 8

To simplify the expression \(2a - 4b + 7 + 8a + 6b - 2\), follow these steps:

1. **Combine the \(a\) terms:**
\[
2a + 8a = 10a
\]

2. **Combine the \(b\) terms:**
\[
-4b + 6b = 2b
\]

3. **Combine the constant terms:**
\[
7 - 2 = 5
\]

Putting it all together, the simplified expression is:
\[
10a + 2b + 5
\]

So the correct response is:

**10a + 2b + 5**

Answer 9

To simplify the expression \(\frac{3}{7}x + \frac{2}{7}x\), we can combine the like terms.

1. Since both terms have the same denominator and the same variable \(x\), we can add the coefficients:
\[
\frac{3}{7} + \frac{2}{7} = \frac{5}{7}
\]

2. Keep the variable \(x\):
\[
\frac{5}{7}x
\]

So the simplified expression is:
\[
\frac{5}{7}x
\]

The correct response is:

**5/7x** (or Start Fraction 5 over 7 End Fraction x).

Answer 10

To simplify the expression \( \frac{6}{7}c - \frac{5}{9}d - \frac{1}{2}c + \frac{1}{3}d \), we will combine the like terms for \(c\) and \(d\).

### Step 1: Combine the \(c\) terms.
The \(c\) terms are \( \frac{6}{7}c \) and \( -\frac{1}{2}c \).

To combine these, we need a common denominator. The least common denominator (LCD) of 7 and 2 is 14.

Convert \( \frac{6}{7}c \) to have a denominator of 14:
\[
\frac{6}{7}c = \frac{12}{14}c
\]

Convert \( -\frac{1}{2}c \) to have a denominator of 14:
\[
-\frac{1}{2}c = -\frac{7}{14}c
\]

Now combine the \(c\) terms:
\[
\frac{12}{14}c - \frac{7}{14}c = \frac{5}{14}c
\]

### Step 2: Combine the \(d\) terms.
The \(d\) terms are \( -\frac{5}{9}d \) and \( \frac{1}{3}d \).

Convert \( \frac{1}{3}d \) to have a denominator of 9:
\[
\frac{1}{3}d = \frac{3}{9}d
\]

Now combine the \(d\) terms:
\[
-\frac{5}{9}d + \frac{3}{9}d = -\frac{2}{9}d
\]

### Final Result:
Now, putting it all together, we get:
\[
\frac{5}{14}c - \frac{2}{9}d
\]

The correct response is:

**5/14c − 2/9d** (Start Fraction 5 over 14 End Fraction c minus Start Fraction 2 over 9 End Fraction d).

Answer 11

To expand \( 5(y + 2) \) using the distributive property, you multiply \(5\) by each term inside the parentheses:

1. Multiply \(5\) by \(y\):
\[
5 \cdot y = 5y
\]

2. Multiply \(5\) by \(2\):
\[
5 \cdot 2 = 10
\]

Now, combine both results:
\[
5(y + 2) = 5y + 10
\]

So, the expanded expression is:

**5y + 10** (5 y plus 10).