Add: 1/2(x+4)+1/4(4x-2). Answer should be in mixed form.
To simplify the expression, let's distribute and combine like terms:
1/2(x+4) + 1/4(4x-2)
= (1/2 * x) + (1/2 * 4) + (1/4 * 4x) - (1/4 * 2)
= 1/2x + 2 + x - 1/2
= 1/2x + x + 2 - 1/2
= (1/2x + x) + (2 - 1/2)
= (3/2x) + (4/2 - 1/2)
= (3/2x) + (3/2)
= (3x + 3)/2
Therefore, the simplified expression in mixed form is: (3x + 3)/2.
To add the given expression in mixed form, follow these steps:
Step 1: Simplify both fractions individually:
- The first fraction is 1/2(x+4). Expanding the fraction, we get (1/2)x + (1/2)(4) = (1/2)x + 2.
- The second fraction is 1/4(4x-2). Expanding the fraction, we get (1/4)(4x) + (1/4)(-2) = x - (1/2).
Step 2: Add the simplified fractions:
- Combine the like terms: (1/2)x + 2 + x - (1/2).
- Simplify further: (1/2)x + x + 2 - (1/2) = (3/2)x + 2 - (1/2).
Step 3: Combine whole numbers and fractions:
- Add the coefficients of x: (3/2 + 1)x + 2 - (1/2).
- Simplify further: (5/2)x + 2 - (1/2).
Step 4: Combine the remaining fractions and whole number:
- Subtract the fractions: (5/2)x + 2 - (1/2) = (5/2)x + 2 - 1/2 = (5/2)x + 3/2.
Therefore, the sum of the given expression is (5/2)x + 3/2 in mixed form.
To add the given expression 1/2(x+4) + 1/4(4x-2), we need to first simplify each term separately and then combine them.
Let's simplify the first term: 1/2(x+4)
To do this, we distribute 1/2 to each term inside the parentheses:
1/2 * x + 1/2 * 4
This simplifies to:
x/2 + 2/2
Simplifying further, we get:
x/2 + 1
Now let's simplify the second term: 1/4(4x-2)
Again, we distribute 1/4 to each term inside the parentheses:
1/4 * 4x - 1/4 * 2
This simplifies to:
4x/4 - 2/4
Simplifying further:
x - 1/2
Now that we have both terms simplified, we can add them together:
(x/2 + 1) + (x - 1/2)
To combine like terms, we can group the "x" terms and the constant terms:
x/2 + x + 1 - 1/2
Combining the "x" terms, we get:
(1/2 + 2/2)x + 1 - 1/2
Simplifying the fractions, we have:
(3/2)x + 1 - 1/2
Now, let's combine the constant terms:
(3/2)x + (2/2 - 1/2)
Simplifying the fractions, we get:
(3/2)x + 1/2
Finally, we can rewrite this in mixed form:
1 and 1/2x
Therefore, the final answer in mixed form is 1 and 1/2x.