Question

Use the properties of operations to add 9(k+1/3)+10(1/2k−1).(1 point)
Responses

14k−2/3
14 k minus Start Fraction 2 over 3 End Fraction

14k−7
14 k minus 7

14k+13
14 k plus 13

19 1/2k−2/3

Answer 1

Use the properties of operations to add 4(g−2)+(g+2).(1 point)
Responses

5g+10
5 g plus 10

5g
5 g

5g−10
5 g minus 10

5g−6

Answer 2

Use the properties of operations to subtract (h+k)−(2k−h) .(1 point)
Responses

2h+k
2 h plus k

−k
negative k

2h−k
2 h minus k

−2h−k

Answer 3

Use the properties of operations to subtract (p−3)−(2.4+2p).(1 point)
Responses

p−5.4
p minus 5.4

−p+5.4
negative p plus 5.4

3p−5.4
3 p minus 5.4

−p−5.4

Answer 4

Subtract: 2(k−4)−3(2k−1) .(1 point)
Responses

−4k−5
negative 4 k minus 5

8k−11
8 k minus 11

−6k−18
negative 6 k minus 18

−4k−11
negative 4 k minus 11

Answer 5

are sure all of the answers above are correct

Answer 6

To simplify the expression \(9\left(k + \frac{1}{3}\right) + 10\left(\frac{1}{2}k - 1\right)\), we can use the distributive property to expand both terms.

1. Expand the first term:
\[
9\left(k + \frac{1}{3}\right) = 9k + 9\left(\frac{1}{3}\right) = 9k + 3
\]

2. Expand the second term:
\[
10\left(\frac{1}{2}k - 1\right) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10
\]

3. Now, combine the results:
\[
9k + 3 + 5k - 10
\]

4. Combine like terms:
\[
(9k + 5k) + (3 - 10) = 14k - 7
\]

So, the final result is:
\[
\boxed{14k - 7}
\]

Answer 7

To simplify the expression \(4(g - 2) + (g + 2)\), we will use the distributive property and combine like terms.

1. Expand \(4(g - 2)\):
\[
4(g - 2) = 4g - 8
\]

2. The second term is already expanded:
\[
g + 2
\]

3. Combine the two results:
\[
(4g - 8) + (g + 2)
\]

4. Combine like terms:
\[
(4g + g) + (-8 + 2) = 5g - 6
\]

So, the final result is:
\[
\boxed{5g - 6}
\]

Answer 8

To simplify the expression \((h + k) - (2k - h)\), we will distribute the negative sign and then combine like terms.

1. Rewrite the expression:
\[
(h + k) - (2k - h) = (h + k) - 2k + h
\]

2. Now, combine the terms:
\[
h + h + k - 2k = 2h + k - 2k
\]

3. Combine like terms:
\[
2h + (k - 2k) = 2h - k
\]

So the final result is:
\[
\boxed{2h - k}
\]

Answer 9

To simplify the expression \((p - 3) - (2.4 + 2p)\), we will distribute the negative sign and then combine like terms.

1. Rewrite the expression:
\[
(p - 3) - (2.4 + 2p) = (p - 3) - 2.4 - 2p
\]

2. Now, combine the terms:
\[
p - 2p - 3 - 2.4
\]

3. Combine the like terms:
- For the \(p\) terms: \(p - 2p = -p\)
- For the constant terms: \(-3 - 2.4 = -5.4\)

Putting it all together:
\[
-p - 5.4
\]

So the final result is:
\[
\boxed{-p - 5.4}
\]

Answer 10

To simplify the expression \(2(k - 4) - 3(2k - 1)\), we will first distribute the constants and then combine like terms.

1. Distribute \(2\) in the first term:
\[
2(k - 4) = 2k - 8
\]

2. Distribute \(-3\) in the second term:
\[
-3(2k - 1) = -6k + 3
\]

3. Now, combine the two results:
\[
(2k - 8) + (-6k + 3)
\]

4. Combine like terms:
- For the \(k\) terms: \(2k - 6k = -4k\)
- For the constant terms: \(-8 + 3 = -5\)

So we have:
\[
-4k - 5
\]

Thus, the final result is:
\[
\boxed{-4k - 5}
\]

Answer 11

Let's carefully review the previous calculations together to ensure they are accurate. I'll go through each of the expressions again, step by step.

### 1. Expression: \(4(g−2)+(g+2)\)

**Simplification:**
1. Expand \(4(g - 2)\):
\[
4g - 8
\]

2. Add the second term:
\[
4g - 8 + g + 2
\]

3. Combine like terms:
\[
(4g + g) + (-8 + 2) = 5g - 6
\]

**Final Result:** \(5g - 6\) (Correct)

### 2. Expression: \((h+k)−(2k−h)\)

**Simplification:**
1. Rewrite as:
\[
h + k - (2k - h) = h + k - 2k + h
\]

2. Combine like terms:
\[
(h + h) + (k - 2k) = 2h - k
\]

**Final Result:** \(2h - k\) (Correct)

### 3. Expression: \((p−3)−(2.4+2p)\)

**Simplification:**
1. Rewrite the expression:
\[
p - 3 - (2.4 + 2p) = p - 3 - 2.4 - 2p
\]

2. Combine like terms:
\[
(p - 2p) + (-3 - 2.4) = -p - 5.4
\]

**Final Result:** \(-p - 5.4\) (Correct)

### 4. Expression: \(2(k−4)−3(2k−1)\)

**Simplification:**
1. Expand \(2(k - 4)\):
\[
2k - 8
\]

2. Expand \(-3(2k - 1)\):
\[
-6k + 3
\]

3. Combine the results:
\[
(2k - 8) + (-6k + 3) = 2k - 6k - 8 + 3
\]
\[
-4k - 5
\]

**Final Result:** \(-4k - 5\) (Correct)

---

**Conclusion:**
All the answers I provided in previous responses are indeed correct:

1. \(5g - 6\)
2. \(2h - k\)
3. \(-p - 5.4\)
4. \(-4k - 5\)

If you have any specific doubts or additional questions, feel free to ask!