Add: 1/2 (x + 4) + 1/4 (4x - 2). Answer should be in mixed number form.
To simplify the expression, let's start by applying the distributive property:
1/2 (x + 4) = 1/2 * x + 1/2 * 4 = 1/2 * x + 2
1/4 (4x - 2) = 1/4 * 4x + 1/4 * (-2) = 1x - 1/2
Now we can combine like terms:
1/2 x + 2 + 1x - 1/2 = (1/2 x + 1x) + (2 - 1/2) = (3/2)x + 3/2 = 3/2(x + 1)
Therefore, the simplified expression is 3/2(x + 1).
Is that in mixed number form??
Apologies for the confusion. Let's convert the expression to mixed number form.
Starting with the simplified expression: 3/2(x + 1)
We can distribute the 3/2 to get: 3/2 * x + 3/2 * 1
3/2 * x = 3/2x
3/2 * 1 = 3/2
Combining these terms, we have: 3/2x + 3/2
To write this in mixed number form, we need to convert the improper fraction (3/2) to a mixed number.
Dividing 3 by 2, we get 1 with a remainder of 1. This remainder becomes the numerator, and the divisor becomes the denominator.
Thus, the mixed number form of the expression is: 1 1/2x + 1 1/2.
Add (4d - 3) + (12d + 4)
To add (4d - 3) + (12d + 4), we can combine like terms:
4d + 12d = 16d
-3 + 4 = 1
Therefore, the sum is 16d + 1.
Add (2m - 3) + (3n - 1) + (3m + 1)
To add (2m - 3) + (3n - 1) + (3m + 1), we can combine like terms:
2m + 3m = 5m
-3 + 1 = -2
The term (3n) does not have any like terms to combine with, so it remains as is.
Therefore, the sum is 5m + 3n - 2.
That was wrong 😞
Apologies for the mistake. Let's redo the addition correctly.
(2m - 3) + (3n - 1) + (3m + 1)
Combining like terms:
2m + 3m = 5m
-3 + 1 + 1 = -1
For (3n), since there are no other n terms to combine with, it remains as is.
Therefore, the correct sum is 5m + 3n - 1.