Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form
To solve the expression 1/2(x+4) + 1/4(4x-2), we first distribute the fractions:
1/2(x+4) + 1/4(4x-2) = 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplifying further:
= (1/2)x + (1/2)*4 + (1/4)*4x - (1/4)*2
= (1/2)x + 2 + x - 1/2
= (1/2)x + x + 2 - 1/2
= (1/2 + 2/2)x + 4/2 - 1/2
= (3/2)x + 4/2 - 1/2
= (3/2)x + 3/2
= (3x + 3)/2
Therefore, the answer in mixed number form is (3x + 3)/2.
To add the given expression, 1/2(x+4)+1/4(4x−2), we'll first simplify each term separately and then combine them together.
Simplifying the first term:
1/2(x+4) can be expanded to 1/2 * x + 1/2 * 4, which results in x/2 + 2.
Simplifying the second term:
1/4(4x−2) can be expanded to 1/4 * 4x - 1/4 * 2, which simplifies to x - 1/2.
Now, we can combine the simplified terms:
x/2 + 2 + x - 1/2.
To combine the terms, we need to obtain a common denominator. Here, the least common denominator is 2.
So, the expression becomes:
(x/2) + 2 + (2x/2) - (1/2).
Combining the like terms:
(x + 2x)/2 + (2 - 1)/2
(3x)/2 + 1/2
Now, let's convert the improper fraction to mixed number form:
(3x + 1)/2
Thus, the final answer in mixed number form is (3x + 1)/2.
To add the expression 1/2(x+4) + 1/4(4x−2), we need to simplify each term first and then combine like terms.
Step 1: Simplify the first term: 1/2(x+4)
Distribute 1/2 to both terms inside the parentheses.
(1/2) * x + (1/2) * 4
x/2 + 2/2
x/2 + 1
Step 2: Simplify the second term: 1/4(4x−2)
Distribute 1/4 to both terms inside the parentheses.
(1/4) * 4x + (1/4) * -2
4x/4 - 2/4
x - 1/2
Step 3: Combine like terms:
(x/2 + 1) + (x - 1/2)
To add x/2 + x, we need a common denominator. The least common multiple of 2 and 1 is 2, so we multiply the first term's numerator and denominator by 2 to have a common denominator of 2.
((x/2) * 2 + 1 * 2) + (x - 1/2)
(x + 2)/2 + x - 1/2
Now, we can combine the fractions:
[(x + 2) + (2x - 1)]/2
(x + 2 + 2x - 1)/2
(3x + 1)/2
The sum of the expression, 1/2(x+4) + 1/4(4x−2), in mixed number form is (3x + 1)/2.