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

Answer 1

To simplify the given expression, we need to combine like terms:

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

Distribute the 1/2 to (x+4) and distribute the 1/4 to (4x-2):

1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2

Simplify each term:

1/2 * x = 1/2x
1/2 * 4 = 2
1/4 * 4x = x
1/4 * 2 = 1/2

So the expression becomes:

1/2x + 2 + x - 1/2

Combine like terms:

1/2x + x = 3/2x

The expression becomes:

3/2x + 2 - 1/2

The denominators are now different. To add the fractions, we need to find a common denominator. The least common denominator (LCD) for 2 and 2 is 2:

(3/2)x + (2 * 2/2) - (1/2)

Simplify:

(3/2)x + 4/2 - 1/2

Now the denominators are all the same, so we can combine the fractions:

(3x/2) + (4 - 1)/2

Simplify:

(3x/2) + 3/2

Since the denominators are the same, we can combine the numerators:

(3x + 3)/2

So the simplified expression is (3x + 3)/2.

Answer 2

wrong

Answer 3

Apologies for the incorrect response. Let's redo the simplification correctly.

To simplify the given expression, we need to combine like terms:

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

Distribute the 1/2 to (x+4) and distribute the 1/4 to (4x-2):

1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2

Simplify each term:

1/2 * x = 1/2x
1/2 * 4 = 4/2 = 2
1/4 * 4x = 4/4x = x
1/4 * 2 = 2/4 = 1/2

So the expression becomes:

1/2x + 2 + x - 1/2

Combine like terms:

1/2x + x = 3/2x

The expression becomes:

3/2x + 2 - 1/2

Now, we need to find a common denominator for 2 and 2, which is 2:

(3/2x) + (2 * 2/2) - (1/2)

Simplify:

3/2x + 4/2 - 1/2

Now that the denominators are the same, we can combine the numerators:

(3/2x + 4 - 1)/2

Combine like terms in the numerator:

(3/2x + 3)/2

To convert this fraction into a mixed number form, we divide 3 by 2:

3 ÷ 2 = 1 remainder 1

Therefore, the expression in mixed number form is:

1 1/2x + 1/2

Answer 4

Add: (4d−3)+(12d+4) .

Answer 5

To add the expressions (4d-3) and (12d+4), we simply combine the like terms:

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

Combining like terms:

4d + 12d - 3 + 4

Combine the terms with "d":
(4d + 12d) + (-3 + 4) = 16d + 1

Therefore, the sum of (4d-3) and (12d+4) is 16d + 1.

Answer 6

Add: (2m−3)+(3n−1)+(3m+1) .

Answer 7

To add the expressions (2m-3), (3n-1), and (3m+1), we need to combine the terms with the same variables:

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

Combining terms with "m":
2m + 3m

Combining terms with "n":
3n

Combining constant terms:
-3 - 1 + 1

Simplifying each part:

2m + 3m = 5m
3n
-3 - 1 + 1 = -3

Therefore, the sum of (2m-3), (3n-1), and (3m+1) is:

5m + 3n - 3

Answer 8

Subtract: 2(10b+4)−(b−2) .

Answer 9

To subtract the expression 2(10b+4) - (b-2), we need to distribute the 2 and then combine like terms:

First, distribute the 2 to (10b+4):
2 * 10b + 2 * 4 = 20b + 8

Now, distribute the negative sign to (b-2):
-1 * b + -1 * -2 = -b + 2

The expression becomes:
20b + 8 - (b + 2)

To remove the parentheses, distribute the negative sign to each term inside the parentheses:
20b + 8 - b - 2

We can combine like terms:
(20b - b) + (8 - 2) = 19b + 6

Therefore, the result of subtracting 2(10b+4) - (b-2) is 19b + 6.

Answer 10

Subtract: (3g−4)−2(3g+4) .

Answer 11

To subtract the expression (3g-4) - 2(3g+4), we need to distribute the -2 and then combine like terms:

First, distribute the -2 to (3g+4):
-2 * 3g - 2 * 4 = -6g - 8

Now, subtract the expression (3g-4) and the distributed expression -6g - 8:
(3g - 4) - (-6g - 8)

To remove the double negative, we can rewrite the subtraction of (-6g - 8) as addition:
(3g - 4) + (6g + 8)

Now, we can combine like terms:
(3g + 6g) + (-4 + 8) = 9g + 4

Therefore, the result of subtracting (3g-4) - 2(3g+4) is 9g + 4.