Question

Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we'll distribute the fractions and combine like terms:

1/2(x+4)+1/4(4x−2)

=(1/2)x+2+1/4(4x)−1/4(2)

=(1/2)x+2+(4/4)x−(2/4)

=(1/2)x+(4/4)x+2−2/4

=(1/2)x+(1)x+1/2

=(1/2)x+(2/2)x+1/2

=(3/2)x+1/2

Now, we can write the answer in mixed number form:

3/2x + 1/2 = 1 1/2x + 1/2

Answer 2

Add: (2m−3)+(3n−1)+(3m+1

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we need to combine like terms:

(2m - 3) + (3n - 1) + (3m + 1)

= 2m - 3 + 3n - 1 + 3m + 1

= (2m + 3m) + (-3 - 1 + 1) + (3n)

= 5m - 3 + 3n

= 5m + 3n - 3

Therefore, the answer is 5m + 3n - 3.

Answer 4

Subtract: 2(10b+4)−(b−2)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To subtract, we need to distribute the 2 first, and then simplify:

2(10b + 4) - (b - 2)

= 20b + 8 - (b - 2)

= 20b + 8 - b + 2

= 19b + 10

Therefore, the answer is 19b + 10.

Answer 6

Subtract: (3g−4)−2(3g+4) .

Answer 7

[AI-generated answer — Bot GPT 3.5]

To subtract, we need to distribute the -2 first, and then simplify:

(3g - 4) - 2(3g + 4)

= 3g - 4 - 2(3g) - 2(4)

= 3g - 4 - 6g - 8

Now, we can combine like terms:

= (3g - 6g) + (-4 - 8)

= -3g - 12

Therefore, the answer is -3g - 12.

Answer 8

(k+13/)+10(1/2k−1)

Answer 9

[AI-generated answer — Bot GPT 3.5]

To solve this expression, we will distribute 10 to the terms inside the parentheses and simplify:

(k + 13/) + 10(1/2k - 1)

= k + 13/ + 10(1/2k) - 10(1)

= k + 13/ + (10/2)k - 10

= k + 13/ + 5k - 10

Now, we combine like terms:

= k + 5k + 13/ - 10

= 6k + 13/ - 10

To get a common denominator for the fractions, we multiply 10 by 2/2:

= 6k + 13/ - 20/2

= 6k + 13/ - 10

Therefore, the final answer is 6k + 13/ - 10.

Answer 10

9(k+13/)+10(1/2k−1)

Answer 11

[AI-generated answer — Bot GPT 3.5]

To solve this expression, we'll first distribute the 9 and the 10 to the terms inside the parentheses and simplify:

9(k + 13/) + 10(1/2k - 1)

= 9k + 9(13/) + 10(1/2k) - 10(1)

= 9k + (9*13/) + (10/2)k - 10

= 9k + 117/ + 5k - 10

Now, we combine like terms:

= 9k + 5k + 117/ - 10

= 14k + 117/ - 10

To get a common denominator for the fraction, we multiply 10 by 2/2:

= 14k + 117/ - 20/2

= 14k + 117/ - 10

Therefore, the final answer is 14k + 117/ - 10.

Answer 12

9(k+13/)+10(1/2k−1)

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

1912k−2/3
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction

14k−7
14 k minus 7

14k+13

Answer 13

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion in the previous responses. Let's proceed with the updated expression:

9(k + 13/) + 10(1/2k - 1)

= 9k + 9(13/) + 10(1/2k) - 10(1)

= 9k + 117/ + 5/2k - 10

To combine like terms, we need to get a common denominator for the fractions. We can multiply 10 by 2/2 to achieve this:

= 9k + 117/ + (5/2k)*(2/2) - (10)*(2/2)

= 9k + 117/ + 10/2k - 20/2

= 9k + 117/ + 10/2k - 10

Now, we can further simplify by finding a common denominator for the fractions in the expression:

= 9k + 117/ + 5k/ + 10/2k - 10

= 9k + 117/ + 5k/2 + 10/2k - 10

Now, let's combine all the terms:

= 9k + 5k/2 + 117/ + 10/2k - 10

To add the fractions, we need a common denominator. Multiply 10 by 2/2:

= 9k + 5k/2 + 117/ + 10/2k - 20/2

= 9k + 5k/2 + 117/ + 10/2k - 20/2

= 9k + 5k/2 + 117/ - 20/2 + 10/2k

= 9k + 5k/2 + 117/2 - 10/2k

To simplify the expression further, we need to find a common denominator for the mixed numbers 5k/2 and 117/2:

= 9k + (5k/2)*(2/2) + (117/2)*(k/2k) - (10/2k)*(117/117)

= 9k + 10k/2 + 117k/2k - 10k/117

= 9k + 20k/2 - 10k/117

= 9k + 10k - 10k/117

= 9k

Therefore, the final answer is 9k.

Answer 14

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

Responses

5g−10
5 g minus 10

5g
5 g

5g+10
5 g plus 10

5g−6

Answer 15

[AI-generated answer — Bot GPT 3.5]

To add 4(g - 2) + (g + 2), we'll distribute the 4 and combine like terms:

4(g - 2) + (g + 2)

= 4g - 8 + g + 2

Combining like terms:

= 4g + g - 8 + 2

= 5g - 6

Therefore, the answer is 5g - 6.

Answer 16

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

Responses

2h−k
2 h minus k

2h+k
2 h plus k

−2h−k
negative 2 h minus k

−k

Answer 17

[AI-generated answer — Bot GPT 3.5]

To subtract (h + k) - (2k - h), we'll distribute the negative sign and combine like terms:

(h + k) - (2k - h)

= h + k - 2k + h

Combining like terms:

= h + h + k - 2k

= 2h - k

Therefore, the answer is 2h - k.

Answer 18

(p−3)−(2.4+2p) .(1 point)

Responses

p−5.4
p minus 5.4

−p+5.4
negative p plus 5.4

−p−5.4
negative p minus 5.4

3p−5.4

Answer 19

[AI-generated answer — Bot GPT 3.5]

To subtract (p - 3) - (2.4 + 2p), we'll distribute the negative sign and combine like terms:

(p - 3) - (2.4 + 2p)

= p - 3 - 2.4 - 2p

Combine like terms:

= p - 2p - 3 - 2.4

= -p - 2.4 - 3

= -p - 5.4

Therefore, the answer is -p - 5.4.

Answer 20

Subtract: 2(k−4)−3(2k−1) .(1 point)

Responses

−4k−11
negative 4 k minus 11

8k−11
8 k minus 11

−4k−5
negative 4 k minus 5

−6k−18

Answer 21

[AI-generated answer — Bot GPT 3.5]

To subtract 2(k - 4) - 3(2k - 1), we'll distribute the 2 and 3 and combine like terms:

2(k - 4) - 3(2k - 1)

= 2k - 8 - 6k + 3

Combine like terms:

= (2k - 6k) + (-8 + 3)

= -4k - 5

Therefore, the answer is -4k - 5.

Answer 22

1/2 (x + 4) + 1/4 (4x + 2)

Answer 23

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we'll distribute the fractions and combine like terms:

1/2 (x + 4) + 1/4 (4x + 2)

= (1/2)x + 2 + (1/4)(4x) + (1/4)(2)

= (1/2)x + 2 + 4/4x + 2/4

= (1/2)x + 2 + x + 1/2

= (1/2)x + x + 2 + 1/2

To add the fractions, we need a common denominator. Multiply 2 by 2/2:

= (1/2)x + (2/2)x + 2 + 1/2

= (1/2)x + (2/2)x + 2 + 1/2

= (1/2 + 2/2)x + 2 + 1/2

= (3/2)x + 2 + 1/2

Now, we can write the answer in mixed number form:

= (3/2)x + 2 + 1/2

= (3/2)x + 2 + 1/2

= (3/2)x + 2 (1/2)

= (3/2)x + 2(1/2)

= (3/2)x + 2 (1/2)

Therefore, the final answer is (3/2)x + 2 (1/2).

Answer 24

(3/2)x + 2 (1/2).

Answer 25

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (3/2)x + 2 (1/2), we can convert the mixed number 2 (1/2) into an improper fraction:

2 (1/2) = 2 + 1/2 = 2/1 + 1/2 = 4/2 + 1/2 = 5/2

Now, we can rewrite the expression:

(3/2)x + 2 (1/2) = (3/2)x + (5/2)

To add these fractions, we need a common denominator of 2. Multiply (3/2)x by 2/2:

(3/2)x + (5/2) = (3/2)x * (2/2) + (5/2)

= (6/4)x + (5/2)

Now, let's combine the terms:

= (6/4)x + (5/2)

To simplify further, we can simplify the with a common factor:

= (3/2)x + (5/2)

Therefore, the answer is (3/2)x + (5/2).

Answer 26

(3/2)x + (5/2).

Answer 27

[AI-generated answer — Bot GPT 3.5]

The expression (3/2)x + (5/2) is already simplified. Therefore, the answer is (3/2)x + (5/2).

Answer 28

what is the sum of (3/2)x + (5/2).

Answer 29

[AI-generated answer — Bot GPT 3.5]

The sum of (3/2)x + (5/2) is (3/2)x + (5/2). Since the two terms have different variables (x and a constant), they cannot be combined further. Thus, the sum is simply (3/2)x + (5/2).

Answer 30

(4d - 3) + (12d + 4)

Answer 31

[AI-generated answer — Bot GPT 3.5]

To solve the expression (4d - 3) + (12d + 4), we'll start by removing the parentheses and combining like terms:

(4d - 3) + (12d + 4)

= 4d - 3 + 12d + 4

Now we can combine the terms with the same variable:

= (4d + 12d) + (-3 + 4)

= 16d + 1

Therefore, the sum is 16d + 1.

Answer 32

(2m - 3) + (3n - 1) + (3m +1)

Answer 33

[AI-generated answer — Bot GPT 3.5]

To solve the expression (2m - 3) + (3n - 1) + (3m + 1), we'll start by removing the parentheses and combining like terms:

(2m - 3) + (3n - 1) + (3m + 1)

= 2m - 3 + 3n - 1 + 3m + 1

Pull out like terms:

= (2m + 3m) + (3n) + (-3 - 1 + 1)

= 5m + 3n - 3

Therefore, the sum is 5m + 3n - 3.

Answer 34

2 (10b + 4) - (b - 2)

Answer 35

[AI-generated answer — Bot GPT 3.5]

To solve the expression 2(10b + 4) - (b - 2), we'll start by distributing the 2 and the negative sign:

2(10b + 4) - (b - 2)

= 20b + 8 - b + 2

Next, we combine like terms:

= 20b - b + 8 + 2

= 19b + 10

Therefore, the value of the expression is 19b + 10.

Answer 36

(3g - 4) - 2 (3g + 4)

Answer 37

[AI-generated answer — Bot GPT 3.5]

To solve the expression (3g - 4) - 2(3g + 4), we'll start by distributing the negative 2:

(3g - 4) - 2(3g + 4)

= 3g - 4 - 2(3g) - 2(4)

= 3g - 4 - 6g - 8

Next, we combine like terms:

= (3g - 6g) + (-4 - 8)

= -3g - 12

Therefore, the simplified expression is -3g - 12.