To simplify the expression 1/2(x + 4) + 1/4(4x - 2), let's first distribute the coefficients:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + 4/4x - 2/4
Next, we add the like terms together:
= (1/2x + 4/4x) + (2/2 - 2/4)
= (2/4x + 4/4x) + (4/4 - 1/2)
= (6/4x) + (3/4)
Since 6/4x is an improper fraction, we need to convert it into a mixed number. To do this, we divide the numerator (6) by the denominator (4), and the remainder becomes the numerator of the fraction part:
= 1 and 2/4x + 3/4
Now, we can simplify the fraction by dividing its numerator and denominator by their greatest common divisor, which is 2:
= 1 and 1/2x + 3/2
So, in mixed number form, the expression 1/2(x + 4) + 1/4(4x - 2) simplifies to 1 and 1/2x + 3/2.
Add 1/2(x + 4) + 1/4(4x - 2). Answer should be in mixed number form
5 answers
That’s wrong
Apologies for the incorrect response. Let's try to simplify the expression correctly.
Given: 1/2(x + 4) + 1/4(4x - 2)
First, let's distribute the coefficients:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + x - 1/2
Now, let's simplify the fraction:
= 1/2x + 1 + x - 1/2
Combining like terms:
= 1/2x + x + 1 - 1/2
= (1/2x + 2x) + (1 - 1/2)
= (3/2x) + (1/2)
In mixed number form, the expression 1/2(x + 4) + 1/4(4x - 2) simplifies to 3/2x + 1/2.
Given: 1/2(x + 4) + 1/4(4x - 2)
First, let's distribute the coefficients:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + x - 1/2
Now, let's simplify the fraction:
= 1/2x + 1 + x - 1/2
Combining like terms:
= 1/2x + x + 1 - 1/2
= (1/2x + 2x) + (1 - 1/2)
= (3/2x) + (1/2)
In mixed number form, the expression 1/2(x + 4) + 1/4(4x - 2) simplifies to 3/2x + 1/2.
That is also wrong
Apologies for the confusion. Let's simplify the expression correctly.
Given: 1/2(x + 4) + 1/4(4x - 2)
First, let's distribute the coefficients:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + x - 1/2
= 1/2x + 1 + x - 1/2
Next, let's combine like terms:
= (1/2x + x) + (1 - 1/2)
= (3/2x) + (1/2)
To convert this into mixed number form, we need to find the whole number and the fractional part.
The numerator, 3, is greater than the denominator, 2. So, we can divide 3 by 2:
3 ÷ 2 = 1 remainder 1
The whole number part is 1, and the fractional part is 1/2.
Thus, in mixed number form, the expression becomes:
1 + 1/2x + 1/2
Given: 1/2(x + 4) + 1/4(4x - 2)
First, let's distribute the coefficients:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + x - 1/2
= 1/2x + 1 + x - 1/2
Next, let's combine like terms:
= (1/2x + x) + (1 - 1/2)
= (3/2x) + (1/2)
To convert this into mixed number form, we need to find the whole number and the fractional part.
The numerator, 3, is greater than the denominator, 2. So, we can divide 3 by 2:
3 ÷ 2 = 1 remainder 1
The whole number part is 1, and the fractional part is 1/2.
Thus, in mixed number form, the expression becomes:
1 + 1/2x + 1/2