1/2(x+4)+1/4(4x-2
To solve this equation, we need to simplify the expression on the right side first.
1/2(x+4) + 1/4(4x-2)
First, distribute the 1/2 to the terms inside the parentheses on the first fraction:
1/2 * x + 1/2 * 4 + 1/4(4x-2)
Simplifying, we get:
x/2 + 2/2 + 1/4(4x-2)
x/2 + 1 + 1/4(4x-2)
Next, distribute the 1/4 to the terms inside the parentheses on the second fraction:
x/2 + 1 + 1/4 * 4x - 1/4 * 2
Simplifying, we get:
x/2 + 1 + x - 1/2
Combine like terms:
x/2 + x + 1 - 1/2
Simplifying, we get:
(x + 2x)/2 + 1 - 1/2
Combine like terms:
3x/2 + 1 - 1/2
Next, find a common denominator for the fractions:
3x/2 + 2/2 - 1/2
Simplifying, we get:
(3x + 2 - 1)/2
Combine like terms:
(3x + 1)/2
as a mixed number
To convert the expression (3x + 1)/2 into a mixed number, we divide the numerator by the denominator and express the result as a whole number and a proper fraction.
Dividing 3x + 1 by 2, we get:
(3x + 1)/2 = 3x/2 + 1/2
Since the numerator is already smaller than the denominator, we can leave it as is.
The expression as a mixed number is:
3x/2 + 1/2
To simplify the given expression: 1/2(x+4) + 1/4(4x-2)
Step 1: Distribute 1/2 to (x+4).
1/2 * x = (1/2)x
1/2 * 4 = 2
So, the first part becomes: (1/2)x + 2
Step 2: Distribute 1/4 to (4x-2).
1/4 * 4x = (1/4)(4x) = x
1/4 * -2 = -1/2
So, the second part becomes: x - 1/2
Step 3: Combine the simplified parts.
(1/2)x + 2 + x - 1/2
Step 4: Combine like terms.
(1/2)x + x + 2 - 1/2
Step 5: Simplify.
(3/2)x + 2 - 1/2
Step 6: Combine like terms again.
(3/2)x + 2 - 1/2
Step 7: Simplify further.
(3/2)x + 3/2
Thus, the simplified expression is (3/2)x + 3/2.
To simplify the expression 1/2(x+4) + 1/4(4x-2), we need to distribute the coefficients to each term within the parentheses and then combine like terms.
Step 1: Distribute 1/2 to (x+4)
(1/2) * x = (1/2)x
(1/2) * 4 = 2
So, 1/2(x+4) becomes (1/2)x + 2.
Step 2: Distribute 1/4 to (4x-2)
(1/4) * 4x = x
(1/4) * (-2) = -2/4 = -1/2
So, 1/4(4x-2) becomes x - 1/2.
Final Step: Combine like terms
(1/2)x + 2 + x - 1/2
To combine the terms, we can add like terms and simplify fractions.
(1/2)x + x + 2 - 1/2
(1/2 + 2/2)x + (4/2 - 1/2)
(3/2)x + (3/2)
Therefore, the simplified form of 1/2(x+4) + 1/4(4x-2) is (3/2)x + (3/2).