bot Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.(1 point)
To add the given expressions, we need to combine like terms.
First, let's simplify each term separately.
For the first term, 1/2(x + 4), we can distribute the 1/2 to the terms inside the parentheses:
1/2(x + 4) = 1/2 * x + 1/2 * 4 = (1/2)x + 2
For the second term, 1/4(4x - 2), we can distribute the 1/4 to the terms inside the parentheses:
1/4(4x - 2) = 1/4 * 4x + 1/4 * (-2) = x - 1/2
Now we can add the simplified terms:
(1/2)x + 2 + x - 1/2
Combining like terms:
(1/2 + 1)x + 2 - 1/2
(3/2)x + 3/2
To express the answer in mixed number form, we can divide the coefficient (3/2) by the denominator (2).
(3/2) ÷ 2 = 3/4
Therefore, the simplified expression in mixed number form is:
3/4x + 3/2
Add: (4d−3)+(12d+4) . (1 point)
To add the given expressions, we need to combine like terms:
(4d - 3) + (12d + 4)
In the first set of parentheses, there is a negative sign in front of 3. We can rewrite it as -3.
Now we can add the like terms:
4d + 12d - 3 + 4
Combining 4d and 12d gives us 16d:
16d - 3 + 4
Simplifying further:
16d + 1
Therefore, the simplified expression is:
16d + 1
Add: (2m−3)+(3n−1)+(3m+1) .(1 point)
To add the given expressions, we need to combine like terms:
(2m - 3) + (3n - 1) + (3m + 1)
First, let's group the terms that have the same variables together:
(2m + 3m) + (-3 - 1 + 1) + (3n)
Combining like terms:
(5m) + (-3 - 1 + 1) + (3n)
Simplifying further:
(5m) + (-3 + 1) + (3n)
(-3 + 1) simplifies to -2:
(5m) - 2 + (3n)
Therefore, the simplified expression is:
5m - 2 + 3n
wrong
Apologies for the mistake. Let's go through the addition again:
To add the given expressions, we need to combine like terms:
(2m - 3) + (3n - 1) + (3m + 1)
First, let's group the terms that have the same variables together:
(2m + 3m) + (-3 + 1) + (3n + 1)
Combining like terms:
5m - 2 + 3n + 1
Now, let's simplify further:
5m + 3n - 1
Therefore, the simplified expression is:
5m + 3n - 1
wrong!
Apologies for the misunderstanding. Let's go through the addition again:
To add the given expressions, we need to combine like terms:
(2m - 3) + (3n - 1) + (3m + 1)
First, let's group the terms that have the same variables together:
(2m + 3m) + (-3 + 1) + (3n + 1)
Combining like terms:
5m - 2 + 3n + 1
Now, let's simplify further:
5m + 3n - 1
Therefore, the simplified expression is:
5m + 3n - 1