Add: 1/2(x+4)+14(4x−2). Answer should be in mixed number form.(1 point)
To solve this equation, we will distribute and simplify first.
Here is the original expression:
1/2(x+4)+14(4x−2)
Distribute 14 to both terms inside the parentheses:
1/2(x+4) + 56x - 28
Now distribute 1/2 to both terms inside its parentheses:
(1/2)(x) + (1/2)(4) + 56x - 28
(1/2)x + 2/2 + 56x - 28
(1/2)x + 1 + 56x - 28
Next, combine like terms:
(1/2)x + 56x + 1 - 28
(1/2)x + 56x - 27
Finally, multiply the whole number (56) by the denominator (2) and add the numerator (1) to get an improper fraction:
(1/2)x + (56*2 + 1)/2 - 27
(1/2)x + 113/2 - 27
To subtract mixed numbers, we need to find a common denominator. In this case, the common denominator is 2:
(1/2)x - (27*2)/2 + 113/2
(1/2)x - 54/2 + 113/2
Combine the fractions with the same denominator:
(1/2)x - 54/2 + 113/2
(1/2)x + 59/2
Therefore, the answer in mixed number form is (1/2)x + 59/2.
To add the given expression, 1/2(x+4) + 14(4x-2), we need to distribute the coefficients and simplify as follows:
Firstly, let's distribute the coefficient 1/2 to (x+4):
1/2(x+4) = (1/2) * x + (1/2) * 4 = 1/2 * x + 2
Now let's distribute the coefficient 14 to (4x-2):
14(4x-2) = 14 * 4x - 14 * 2 = 56x - 28
Now we can add the two simplified expressions:
(1/2) * x + 2 + 56x - 28
Combining like terms, we have:
(1/2) * x + 56x + 2 - 28
Simplifying further:
(1/2) * x + 56x - 26
To express the answer in mixed number form, we can rewrite (1/2) as a mixed number:
(1/2) = 0.5 = 0 + 1/2
So the final answer in mixed number form is:
0 + 1/2 * x + 56x - 26
To add the expression 1/2(x+4)+14(4x−2), we need to simplify each term and then combine them.
Let's start with the first term: 1/2(x+4). To simplify this, we distribute the 1/2 to both terms inside the parentheses:
1/2(x+4) = 1/2 * x + 1/2 * 4 = (1/2)x + 2
Next, let's simplify the second term: 14(4x−2). Here, we again distribute the 14 to both terms inside the parentheses:
14(4x−2) = 14 * 4x + 14 * (-2) = 56x - 28
Now, we can rewrite the expression with the simplified terms:
(1/2)x + 2 + 56x - 28
To combine like terms, we add the coefficients of x:
(1/2 + 56)x + (2 - 28)
1/2 + 56 = 56.5 (mixed number form)
So, the simplified expression is:
56.5x - 26