Add: 1/2 * (x + 4) + 1/4 * (4x - 2)
Answer should be in mixed number form. (1 pointAdd: 1/2 * (x + 4) + 1/4 * (4x - 2)
Answer should be in mixed number form. (1 point
wrong
Wrong
To solve this, we first distribute and simplify each term within the parentheses:
1/2 * (x + 4) = (1/2 * x) + (1/2 * 4) = 1/2 * x + 2
1/4 * (4x - 2) = (1/4 * 4x) + (1/4 * -2) = x - 1/2
Now we can combine the two simplified terms:
(1/2 * x + 2) + (x - 1/2) = 1/2 * x + x + 2 - 1/2 = 3/2 * x + 3/2
The final answer in mixed number form is 3/2 * x + 3/2.
To solve the expression and represent the answer in mixed number form, follow these steps:
1. Distribute the coefficients:
Multiply 1/2 by (x + 4) and 1/4 by (4x - 2).
1/2 * (x + 4) = 1/2 * x + 1/2 * 4 = 1/2 * x + 2/2 = 1/2 * x + 1
1/4 * (4x - 2) = 1/4 * 4x - 1/4 * 2 = x - 1/2
2. Combine like terms:
Combine the x terms and the constant terms separately.
x + 1/2 * x = 3/2 * x
1 + (-1/2) = 1/2 * 2 - 1/2 = 1 - 1/2 = 1/2
3. Add the like terms:
Add the combined x terms and constant terms.
3/2 * x + 1/2 = 3/2 * x + 1/2
4. Represent the answer in mixed number form:
To convert an improper fraction to a mixed number, divide the numerator by the denominator.
The whole number is found by dividing 3 by 2, which gives us 1.
The remainder is found by taking the numerator (1) modulo the denominator (2), which gives us 1.
Therefore, the answer in mixed number form is 1 1/2.