Add: 1 over 2 (x + 4) + 1 over 4 ( 4 x − 2) Answer should be in mixed number form.
To simplify the expression, first distribute the fractions:
1/2 * (x + 4) + 1/4 * (4x - 2)
= (1/2 * x) + (1/2 * 4) + (1/4 * 4x) + (1/4 * -2)
= (1/2 * x) + 2 + (1/4 * 4x) + (-1/2)
= (1/2 * x) + 2 + (1 * x) + (-1/2)
Next, combine like terms:
= 1/2x + x - 1/2 + 2
= (3/2)x + 3/2
In mixed number form, this can be written as:
1 and 1/2x
it says its wrong
To add the given expressions in mixed number form, follow these steps:
Step 1: Simplify each fraction by finding a common denominator.
The denominators are 2 and 4, which have a common multiple of 4.
1/2 (x + 4) = (2/4)(x + 4)
1/4 (4x − 2) = (1/4)(4x) − (1/4)(2) = (4/4)x − (1/2)
Step 2: Combine the fractions with the same denominator:
(2/4)(x + 4) + (4/4)x − (1/2)
Step 3: Simplify further:
(2/4)x + (8/4) + (4/4)x − (1/2)
(6/4)x + (8/4) − (1/2)
Step 4: Combine like terms:
(6x + 8 - 2) / 4
(6x + 6) / 4
Therefore, the answer in mixed number form is:
(6x + 6) / 4
To add the given fractions, we need to find a common denominator. In this case, the common denominator is 4.
Let's rewrite the fractions with the common denominator:
1 over 2 (x + 4) = (1/2)(x + 4) = (2/4)(x + 4)
1 over 4 (4x − 2) = (1/4)(4x - 2) = (1/4)(4x - 2)
Now, we can add the fractions by combining the numerators:
(2/4)(x + 4) + (1/4)(4x - 2)
Expand each fraction:
(2/4)x + (2/4)(4) + (1/4)(4x) - (1/4)(2)
Simplify each term:
(1/2)x + (8/4) + (4/4)x - (2/4)
Now, combine the terms with the same variable:
(1/2 + 4/4)x + (8/4 - 2/4)
Simplify the fractions:
(6/4)x + (6/4)
Now, we can simplify the fraction if possible:
(3/2)x + (3/2)
The answer in mixed number form is:
3/2(x + 1)