add: 1/2(x+4)+1/4(4x−2) . answer should be in mixed number form
wrong the answer is 1 1/2x+1 1/2
To simplify the given expression, let's start by finding a common denominator for the fractions:
The least common multiple of 2 and 4 is 4.
1/2(x+4) can be written as 2/4(x+4)
1/4(4x-2) remains the same.
Now, let's simplify the expression:
2/4(x+4) + 1/4(4x−2) can be written as (2(x+4) + 1(4x−2))/4
Distributing the terms:
(2x + 8 + 4x - 2)/4
Combining like terms:
(6x + 6)/4
Now, to express the solution in mixed number form, we can divide the numerator by the denominator:
6x/4 + 6/4 = 3x/2 + 3/2
Therefore, the expression 1/2(x+4) + 1/4(4x−2) simplifies to the mixed number form 3x/2 + 3/2.
Apologies for the mistake. Let's re-evaluate the expression correctly:
To simplify the given expression, let's start by finding a common denominator for the fractions:
The least common multiple of 2 and 4 is 4.
1/2(x+4) can be written as 2/4(x+4)
1/4(4x-2) can be written as 1/4(4x-2)
Now, let's simplify the expression:
2/4(x+4) + 1/4(4x-2) can be written as (2(x+4) + 1(4x-2))/4
Distributing the terms:
(2x + 8 + 4x - 2)/4
Combining like terms:
(6x + 6)/4
Now, let's divide the numerator by the denominator:
(6x + 6)/4 = (6/4)x + (6/4)
Simplifying further:
(6/4)x + (6/4) = (3/2)x + (3/2)
This expression can be further simplified to the mixed number form:
(3/2)x + (3/2) = 1 1/2x + 1 1/2
Therefore, the expression 1/2(x+4) + 1/4(4x−2) simplifies to 1 1/2x + 1 1/2.
To simplify the expression, 1/2(x+4) + 1/4(4x-2), we need to first distribute the fractions into the brackets:
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2/2 = 1/2x + 1
1/4(4x-2) = 1/4 * 4x + 1/4 * (-2) = 4/4x - 2/4 = 1x - 1/2
Now, we can simplify the expression:
1/2x + 1 + 1x - 1/2
Combining like terms:
1/2x + 1x + 1 - 1/2
Adding the x terms:
(1/2 + 1) x + 1 - 1/2
1/2 + 1 = 3/2
So the expression becomes:
(3/2)x + 1 - 1/2
Combining the constant terms:
(3/2)x + 1/2
To convert this into mixed number form, we need to divide the numerator by the denominator:
3 ÷ 2 = 1 remainder 1
Therefore, the final answer in mixed number form is:
1 1/2x + 1/2
To add the given expression, 1/2(x+4) + 1/4(4x-2), we need to simplify each term separately, and then combine them.
Let's start by simplifying the first term, 1/2(x+4):
First, distribute the 1/2 to both terms inside the parentheses:
1/2 * x + 1/2 * 4
This simplifies to:
1/2 * x = x/2
1/2 * 4 = 4/2 = 2
So the first term becomes: x/2 + 2
Now let's simplify the second term, 1/4(4x-2):
Again, distribute the 1/4 to both terms inside the parentheses:
1/4 * 4x + 1/4 * (-2)
This simplifies to:
1/4 * 4x = 4x/4 = x
1/4 * (-2) = -2/4 = -1/2
So the second term becomes: x - 1/2
Now, let's combine the simplified terms:
(x/2 + 2) + (x - 1/2) = x/2 + x + 2 - 1/2
To combine the terms, we need a common denominator for the fractions. The least common denominator (LCD) of 2, 1, and 2 is 2. So, we can rewrite the expression using this common denominator:
(x/2 + x + 2 - 1/2) = (x/2 + 2x/2 + 4/2 - 1/2)
Simplifying further, we get:
(x/2 + 2x/2 + 4/2 - 1/2) = (3x/2 + 3/2)
Now, let's convert the improper fraction to a mixed number:
To convert 3x/2 to a mixed number, divide the numerator (3x) by the denominator (2):
3x ÷ 2 = (3/2)x
So, the final answer in mixed number form is:
(3/2)x + 3/2