Add: 1/2(x+4)+1/4(4x-2). Answer should be in mixed number form. (1 point)
To solve this equation, we need to simplify and combine like terms.
First, let's simplify 1/2(x+4):
1/2(x+4) = 1/2*x + 1/2*4 = 1/2*x + 2
Now, let's simplify 1/4(4x-2):
1/4(4x-2) = 1/4*4x - 1/4*2 = x - 1/2
Now we can combine the two simplified expressions:
1/2(x+4) + 1/4(4x-2) = 1/2*x + 2 + x - 1/2
Next, let's combine like terms:
1/2*x + 1/2*x + 2 - 1/2 = x + 1/4
Now, let's write the final answer in mixed number form. Assuming x is a whole number:
x + 1/4 = x + 0.25
Therefore, the answer in mixed number form is x + 0.25.
That's wrong
Apologies for the previous inaccurate response. Let's try solving the equation correctly.
1/2(x+4) + 1/4(4x-2)
To simplify, we first distribute the fractions to their respective terms:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplifying each term gives us:
x/2 + 2/2 + 4x/4 - 2/4
Combining the like terms with the same denominator:
x/2 + 2/2 + (4x - 2)/4
We can simplify 2/2 to 1:
x/2 + 1 + (4x - 2)/4
We need to find a common denominator for the fractions, which is 4. We rewrite the first term with a denominator of 4:
2x/4 + 1 + (4x - 2)/4
Combining the numerators:
(2x + 4 + 4x - 2)/4
Simplifying further:
(6x + 2)/4
To express this as a mixed number, we divide the numerator by the denominator:
6x/4 + 2/4
= 3x/2 + 1/2
Therefore, the final answer in mixed number form is 3x/2 + 1/2.
To add the given expression, 1/2(x+4) + 1/4(4x-2), you need to first simplify each term separately and then add them together. Let's begin:
1/2(x+4):
To simplify this term, you multiply the coefficients and add the variables:
1/2 * x = x/2
1/2 * 4 = 4/2 = 2
Therefore, 1/2(x+4) simplifies to x/2 + 2.
Now let's simplify the second term:
1/4(4x-2):
Similarly, you multiply the coefficients and distribute them to the variables:
1/4 * 4x = 4x/4 = x
1/4 * -2 = -2/4 = -1/2
Thus, 1/4(4x-2) simplifies to x - 1/2.
Now we can add the two simplified terms together:
(x/2 + 2) + (x - 1/2):
To add these terms, combine the like terms:
x + x/2 + 2 - 1/2:
To simplify, find a common denominator for the fractions:
x + (2x/2) + (4/2 - 1/2):
Now, combine the fractions:
x + 2x/2 + 3/2:
Since 2x/2 equals x, we have:
x + x + 3/2:
Finally, combine the x terms:
2x + 3/2.
The answer in mixed number form is 2x + 3/2.
To simplify this expression and write the answer in mixed number form, we need to follow a few steps:
Step 1: Distribute the coefficients to the terms inside the parentheses.
(1/2)(x + 4) + (1/4)(4x - 2)
= (1/2) * x + (1/2) * 4 + (1/4) * 4x + (1/4) * (-2)
= (1/2)x + 2/2 + 4/4x - 2/4
= (1/2)x + 1 + (1/4)x - 1/2
Step 2: Simplify the fractions by finding a common denominator.
Since the denominators in this expression are 2 and 4, the smallest common denominator is 4.
= (2/4)x + 1 + (1/4)x - 2/4
= (2x/4) + 1 + (1x/4) - 2/4
= (2x + 1 + x - 2)/4
= (3x - 1)/4
Step 3: Convert the improper fraction (3x - 1)/4 into a mixed number.
To convert an improper fraction into a mixed number, divide the numerator by the denominator and express any remainder over the original denominator.
Divide 3x by 4:
3x ÷ 4 = 3/4 * x
Divide -1 by 4:
-1 ÷ 4 = -1/4
Therefore, the converted mixed number form is:
(3/4 * x) - 1/4