Add: 1/2(x+4)+1/4(4x−2)
. Answer should be in mixed number form.
1/2(x+4)+1/4(4x−2)
First, let's simplify each term separately.
1/2(x+4) = (1/2)x + (1/2)(4) = 1/2x + 2
1/4(4x−2) = (1/4)(4x) - (1/4)(2) = x - 1/2
Now, let's combine the simplified terms.
1/2x + 2 + x - 1/2
Next, we need to find a common denominator for 2 and 1/2, which is 2. So we multiply 2 by 1/2 to make it have the same denominator.
1/2x + 2 + 2/2x - 1/2
Now, we can combine the terms.
(1/2x + 2/2x) + (2 - 1/2) = (3/2x) + (3/2)
Therefore, the final answer in mixed number form is 3/2x + 3/2.
nope
Apologies for the mistake in the previous response. Let's solve it correctly.
To add the given expression:
1/2(x+4) + 1/4(4x-2)
Let's start by simplifying each term:
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2
1/4(4x-2) = 1/4 * 4x - 1/4 * 2 = x - 1/2
Now we can combine the simplified terms:
1/2x + 2 + x - 1/2
Combining like terms:
(1/2x + x) + (2 - 1/2) = (3/2x) + (3/2)
Since the coefficients of the variable (x) are the same in both terms, we can combine them:
3/2x + 3/2
To express the answer in mixed number form, divide the coefficients:
3 ÷ 2 = 1 remainder 1
Therefore, the final answer in mixed number form is:
1 1/2x + 1 1/2
To add the given expression, 1/2(x+4) + 1/4(4x-2), we'll begin simplifying each term separately.
First, let's simplify 1/2(x+4):
1/2(x+4) = (1/2)x + (1/2)4 = (1/2)x + 2
Next, let's simplify 1/4(4x-2):
1/4(4x-2) = (1/4)4x - (1/4)2 = x - 1/2
Now, adding the simplified terms:
(1/2)x + 2 + x - 1/2
To add these terms, we need to find a common denominator for the fractions. The least common denominator (LCD) of 2 and 4 is 4. So, let's rewrite the expression with a common denominator:
(2/4)x + 2 + (2/4)x - (1/2)
Combining the like terms, we have:
(2x + 4 + 2x - 2) / 4
Simplifying the numerator:
(4x + 2) / 4
Now we can simplify further by dividing both the numerator and denominator by 2:
(2x + 1) / 2
Finally, let's express the answer in mixed number form:
The mixed number equivalent of (2x + 1) / 2 is 1 1/2x.
To add the given expression, 1/2(x+4) + 1/4(4x−2), we can follow these steps:
Step 1: Distribute the fractions.
To distribute the first fraction, 1/2, to the expression (x+4), you multiply each term inside the parentheses by 1/2:
1/2 * x = 1/2x
1/2 * 4 = 2
Similarly, for the second fraction, 1/4, distribute it to the expression (4x−2):
1/4 * 4x = 1x = x
1/4 * -2 = -1/2
So now the expression becomes: (1/2x + 2) + (x − 1/2)
Step 2: Combine like terms.
Combine the x terms together and the constant terms together:
1/2x + x = (1/2 + 1)x = 3/2x
2 − 1/2 = 3/2
So the expression simplifies to: 3/2x + 3/2
Step 3: Express the answer in mixed number form.
To express the answer in mixed number form, we divide the coefficient in front of x (3/2) by the denominator (2). The quotient becomes the whole number part, and the remainder becomes the numerator of the fraction part.
In this case, the coefficient 3/2 divided by 2 equals 1 with a remainder of 1. Therefore, the answer is:
1 and 1/2