Add: 1/2(x+4)+1/4(4x-2). Answer should be in mixed number form.
To simplify the expression 1/2(x+4)+1/4(4x-2), we can distribute the coefficients:
1/2(x+4) + 1/4(4x-2) = 1/2 * x + 1/2 * 4 + 1/4 * 4x -1/4 * 2
Simplifying further, we get:
1/2 * x = x/2
1/2 * 4 = 4/2 = 2
1/4 * 4x = 4x/4 = x
1/4 * -2 = -2/4 = -1/2
Adding the simplified terms, we find:
x/2 + 2 + x - 1/2
Combining like terms, we have:
x + x/2 + 2 - 1/2 = 2x/2 + x/2 + 4/2 - 1/2 = (2x+x+4-1)/2 = (3x+3)/2
Therefore, the expression 1/2(x+4)+1/4(4x-2) simplifies to (3x+3)/2 in mixed number form.
Wrong
Apologies for the mistake. Let's solve it correctly this time:
To simplify the expression 1/2(x+4)+1/4(4x-2), we can distribute the coefficients:
1/2(x+4) + 1/4(4x-2) = 1/2 * x + 1/2 * 4 + 1/4 * 4x -1/4 * 2
Simplifying further, we get:
1/2 * x = x/2
1/2 * 4 = 4/2 = 2
1/4 * 4x = 4x/4 = x
1/4 * -2 = -2/4 = -1/2
Adding the simplified terms, we find:
x/2 + 2 + x - 1/2
Combining like terms, we have:
x/2 + x + 2 - 1/2 = (2x + x + 4 - 1)/2 = (3x + 3)/2
Therefore, the expression 1/2(x+4)+1/4(4x-2) simplifies to (3x + 3)/2 in mixed number form.
1/2(×+4)+1/4(4×-2. The answer should be in mixed number form
To solve 1/2(x+4) + 1/4(4x-2) and express the answer in mixed number form:
Let's simplify each term first:
1/2(x+4) = 1/2 * x + 1/2 * 4 = x/2 + 2
1/4(4x-2) = 1/4 * 4x - 1/4 * 2 = x - 1/2
Now we can rewrite the expression as:
(x/2 + 2) + (x - 1/2)
Combining the like terms, we get:
x/2 + x + 2 - 1/2
Next, we can add the coefficients and simplify:
2x/2 + 2 - 1/2 = x + 2 - 1/2
To simplify the expression involving mixed numbers:
2 - 1/2 = 2 - 1/2 = 4/2 - 1/2 = 3/2
Therefore, the final answer in mixed number form is:
x + 3/2
Wrong I need the answer
Apologies for the confusion. Let's solve it correctly:
To simplify the expression 1/2(x+4) + 1/4(4x-2) and express the answer in mixed number form:
First, let's distribute the coefficients:
1/2(x+4) + 1/4(4x-2) = 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplifying each term:
1/2 * x = x/2
1/2 * 4 = 4/2 = 2
1/4 * 4x = 4x/4 = x
1/4 * -2 = -2/4 = -1/2
Now, we can rewrite the expression as:
x/2 + 2 + x - 1/2
Combining the like terms:
x + x/2 + 2 - 1/2 = (2x+x+4-1)/2 = (3x+3)/2
As requested, let's express the answer in mixed number form:
We divide the numerator (3x+3) by the denominator (2). The quotient will be the whole number part, and the remainder will be the numerator of the fraction part.
The whole number part is given by the division: (3x+3) ÷ 2.
The remainder is the numerator: Remainder: (3x+3) % 2.
So, the mixed number form of the expression 1/2(x+4) + 1/4(4x-2) is:
(3x+3) ÷ 2 + (3x+3) % 2/2
Please note that the division and remainder expressions may vary depending on the values of x.
Thats wrong
Apologies for the ongoing confusion. Let's solve the expression correctly:
1/2(x+4) + 1/4(4x-2)
To simplify this expression, we can distribute the coefficients:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= x/2 + 2 + x - 1/2
Next, we can combine like terms:
= (x + x/2) + (2 - 1/2)
To add the fractions, we need a common denominator, which is 2:
= (2x/2 + x/2) + (4/2 - 1/2)
= (3x/2) + (3/2)
Now, we can add the two fractions:
= (3x + 3)/2
Therefore, the simplified expression 1/2(x+4) + 1/4(4x-2) is (3x + 3)/2.
To simplify the given expression and get the answer in mixed number form, follow these steps:
1. Distribute the fractions to simplify the expression. Multiply each fraction by the number outside the parenthesis.
(1/2) * (x + 4) + (1/4) * (4x - 2)
2. Simplify the multiplication within each term.
(1/2)(x) + (1/2)(4) + (1/4)(4x) - (1/4)(2)
3. Simplify each term further.
(1/2)x + (2/2) + (4/4)x - (2/4)
Simplify fractions if possible:
x/2 + 2/2 + x - 1/2
4. Combine like terms.
x/2 + 2/2 + x - 1/2
Add the x/2 and x terms:
(x + x/2) + 2/2 - 1/2
Simplify the x + x/2:
(2x/2 + x/2) + 2/2 - 1/2
Combine like terms:
(3x/2) + 2/2 - 1/2
Simplify fractions:
(3x/2) + 1/2
5. Express the answer in mixed number form. To do this, divide 3x by 2:
(3x / 2) ÷ 2
Divide the whole number by the divisor (2), then write the remainder over the divisor.
3 ÷ 2 = 1 remainder 1
The answer is 1 and 1/2.
Therefore, the expression 1/2(x + 4) + 1/4(4x - 2) simplifies to 1 1/2 in mixed number form.