Question

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

12x2
12 x squared

4x + 8
4 x plus 8

12x
12 x

4 + 8x

Answer 1

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

3g + 5h
3 g plus 5 h

−2gh
negative 2 g h

2gh − 4gh
2 g h minus 4 g h

3g − 5h

Answer 2

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

12ab + 5
12 a b plus 5

−2ab + 14ab + 5
negative 2 a b plus 14 a b plus 5

10a − 2b +5
10 a minus 2 b plus 5

10a + 2b +5

Answer 3

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

5/14x
Start Fraction 5 over 14 End Fraction x

5/14x2
Start Fraction 5 over 14 End Fraction x squared

5/7x2
Start Fraction 5 over 7 End Fraction x squared

5/7x

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 minus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c minus 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

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

Answer 5

To simplify \(4x + 8x\), you can combine like terms. Both terms have \(x\) as a variable.

So,

\[
4x + 8x = (4 + 8)x = 12x
\]

The simplified expression is \(12x\).

Among the response options given, the correct one is:

**12x** (12 x).

Answer 6

To simplify \(9g − 7h − 6g + 2h\), we can combine like terms.

1. Combine the \(g\) terms:
\[
9g - 6g = (9 - 6)g = 3g
\]

2. Combine the \(h\) terms:
\[
-7h + 2h = (-7 + 2)h = -5h
\]

Putting it all together, we have:
\[
3g - 5h
\]

Among the response options given, the correct one is:

**3g − 5h**.

Answer 7

To simplify \(2a − 4b + 7 + 8a + 6b − 2\), we can combine like terms step by step.

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, we have:
\[
10a + 2b + 5
\]

Among the response options given, the correct one is:

**10a + 2b + 5**.

Answer 8

To simplify \(\frac{3}{7}x + \frac{2}{7}x\), you can combine the like terms since they both have \(x\) as a common factor.

1. Combine the coefficients:
\[
\frac{3}{7} + \frac{2}{7} = \frac{3 + 2}{7} = \frac{5}{7}
\]

2. Since both terms also include \(x\), we can write:
\[
\frac{5}{7}x
\]

Among the response options given, the correct one is:

**\(\frac{5}{7}x\)** (5/7x).

Answer 9

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

First, let’s group the \(c\) terms and the \(d\) terms separately:

1. **For the \(c\) terms**:
- Combine \( \frac{6}{7}c \) and \( -\frac{1}{2}c \).
- To do this, we need a common denominator. The least common denominator (LCD) for 7 and 2 is 14.

Converting each term:
\[
\frac{6}{7}c = \frac{12}{14}c \quad \text{(since } 6 \times 2 = 12\text{)}
\]
\[
-\frac{1}{2}c = -\frac{7}{14}c \quad \text{(since } 1 \times 7 = 7\text{)}
\]
Now combine:
\[
\frac{12}{14}c - \frac{7}{14}c = \frac{12 - 7}{14}c = \frac{5}{14}c
\]

2. **For the \(d\) terms**:
- Combine \( -\frac{5}{9}d \) and \( \frac{1}{3}d \).
- The least common denominator for 9 and 3 is 9.

Converting:
\[
\frac{1}{3}d = \frac{3}{9}d \quad \text{(since } 1 \times 3 = 3\text{)}
\]
Now combine:
\[
-\frac{5}{9}d + \frac{3}{9}d = \frac{-5 + 3}{9}d = -\frac{2}{9}d
\]

Putting it all together, we have:
\[
\frac{5}{14}c - \frac{2}{9}d
\]

Among the response options given, the correct one is:

**\(\frac{5}{14}c - \frac{2}{9}d\)** (5/14c − 2/9d).