Add 1/2(x+4)+1/4(4x-2)
1/2(x+4)+1/4(4x-2) can be simplified as follows:
1/2(x+4) + 1/4(4x-2)
= (1/2)*(x+4) + (1/4)*(4x-2) (distributing multiplication)
= (1/2)*(x) + (1/2)*(4) + (1/4)*(4x) + (1/4)*(-2) (distributing multiplication further)
= (1/2)*x + (1/2)*4 + (1/4)*4x + (1/4)*(-2) (simplifying multiplication)
= 1/2*x + 2 + (1/4)*4x + (1/4)*(-2) (simplifying addition)
= 1/2*x + 2 + 1*x + (-1/2) (simplifying multiplication and addition further)
= 1/2*x + x + 2 - 1/2 (simplifying the last two constants)
= (1/2 + 1)*x + (2 - 1/2) (combining like terms)
= (3/2)*x + (3/2) (simplifying further)
So, the simplified expression is (3/2)*x + 3/2.
To add the given expression, we need to combine like terms.
Given expression: 1/2(x+4) + 1/4(4x-2)
First, let's distribute the coefficients inside each parentheses:
1/2(x) + 1/2(4) + 1/4(4x) - 1/4(2)
Simplifying further:
1/2x + 2/2 + 4/4x - 2/4
Combining like terms:
1/2x + 1 + x/1 - 1/2
Now, we need to find a common denominator to add the terms together. The common denominator for 2 and 1 is 2.
(1/2)x + (1)*(2/2) + (x/1)*(2/2) - (1/2)*(1/1)
Simplifying further:
(1/2)x + 2/2 + 2x/2 - 1/2
Now, let's combine the terms:
(1/2)x + 2/2 + 2x/2 - 1/2 = x/2 + 2/2 + 2x/2 - 1/2
Simplifying further:
x/2 + 2/2 + 2x/2 - 1/2 = (x + 2 + 2x - 1)/2
Combining the numerators:
(x + 2 + 2x - 1)/2 = (3x + 1)/2
Therefore, the sum of the given expression is (3x + 1)/2.
To simplify the expression 1/2(x+4) + 1/4(4x-2), you need to distribute the fractions.
First, distribute the 1/2 into the expression (x+4):
1/2(x+4) = (1/2 * x) + (1/2 * 4) = (1/2)x + 2
Next, distribute the 1/4 into the expression (4x-2):
1/4(4x-2) = (1/4 * 4x) + (1/4 * -2) = x - 1/2
Now that we have simplified both parts, we can combine them:
(1/2)x + 2 + x - 1/2
To combine these terms, we need to find a common denominator. The least common denominator for 2 and 4 is 4. So, we'll multiply the first term by 2/2 and the second term by 4/4 to get the same denominator:
(1/2)x + 2 + (4/4)x - 1/2
Simplifying the fractions with the common denominator:
(2/4)x + 2 + (4/4)x - 1/2
Combining like terms:
(6/4)x + 2 - 1/2
Adding the coefficients of like terms:
(6/4 + 4/4)x + 2 - 1/2
Simplifying the coefficients:
(10/4)x + 2 - 1/2
Combining the integer and fraction parts:
(10/4)x + (4/4) - (1/2)
Adding the fractions and simplifying:
(10/4)x + (8/4) - (1/2) = (10/4)x + (8/4) - (2/4) = (10/4)x + (6/4)
Since the numerator in each term has a common factor of 2, we can simplify it further by dividing both terms by 2:
(5/2)x + (3/2)
Therefore, the simplified expression is (5/2)x + (3/2).