Add: 12(x+4)+14(4x−2) . Answer should be in mixed number form.(1 point)
: 1/2(x+4)+1/4(4x−2)
To solve the expression 12(x+4)+14(4x-2), we first need to distribute the 12 and 14 to their respective terms inside the parentheses.
12(x+4) = 12x + 48
14(4x-2) = 56x - 28
Next, we combine like terms by adding the terms with the same variable.
12x + 48 + 56x - 28 = 68x + 20
The answer in mixed number form is 68x + 20.
To solve the expression 1/2(x+4)+1/4(4x-2), we first need to distribute the 1/2 and 1/4 to their respective terms inside the parentheses.
1/2(x+4) = (1/2)x + 2
1/4(4x-2) = (1/4)(4x) - (1/4)(2) = x - 1/2
Next, we combine like terms by adding the terms with the same variable.
(1/2)x + 2 + x - 1/2 = (1/2)x + x + 2 - 1/2 = (1/2)x + (2/2)x + 2 - 1/2 = (3/2)x + 3/2
The answer in mixed number form is (3/2)x + 3/2.
To add 12(x+4) and 14(4x-2), we need to distribute the coefficients in both expressions.
First, distribute 12 to (x+4):
12(x+4) = 12*x + 12*4 = 12x + 48
Next, distribute 14 to (4x-2):
14(4x-2) = 14*4x - 14*2 = 56x - 28
Now, we can combine the like terms:
12x + 48 + 56x - 28
To combine the x terms, add the coefficients:
12x + 56x = 68x
Combine the constants:
48 - 28 = 20
The final answer, in mixed number form, is 68x + 20.
To evaluate the expression and get the answer in mixed number form, we can follow these steps:
1. Simplify the expressions within the parentheses:
- For the first expression within the parentheses, we distribute the 12 to the terms inside:
12 * x + 12 * 4 = 12x + 48.
- For the second expression within the parentheses, we distribute the 14 to the terms inside:
14 * 4x + 14 * (-2) = 56x - 28.
2. Combine like terms:
- Combine the 12x and 56x terms: 12x + 56x = 68x.
- Combine the 48 and -28 terms: 48 - 28 = 20.
3. Bring the result into mixed number form:
A mixed number consists of a whole number and a fraction. To convert an improper fraction to a mixed number, divide the numerator by the denominator and express the remainder as a fraction.
In this case, the numerator is 20 and the denominator is 68. Dividing, we get: 20 ÷ 68 = 0 with a remainder of 20.
So, the mixed number form of the answer is: 0 20/68.
Therefore, the result of the expression 12(x+4)+14(4x−2) in mixed number form is 0 20/68.