1/2 (x + 4) + 1/4 (4x - 2)
To simplify the expression 1/2 (x + 4) + 1/4 (4x - 2), we can distribute the fractions and then combine like terms.
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) + (4/4)x - (2/4)
= 1/2 x + 1 + x - 1/2
= 1/2 x + x + 1 - 1/2
= (1/2 + 2/2) x + (1 - 1/2)
= (3/2) x + 1/2
So, the simplified expression is (3/2)x + 1/2.
1/2 (x + 4) + 1/4 (4x - 2) MIXED NUMBER FORM.
To express the expression 1/2 (x + 4) + 1/4 (4x - 2) in mixed number form, we can first simplify the expression and then convert it to mixed number form.
Let's simplify the expression:
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 + (4/4)x - 1/2
= (1/2)x + 1 + x - 1/2
= (1/2)x + x + 1 - 1/2
= (3/2)x + 1/2
Now, let's convert it to mixed number form:
(3/2)x + 1/2
To convert the expression to mixed number form, we can divide the numerator by the denominator. The quotient will be the whole number part, and the remainder will be the numerator of the fractional part.
For (3/2)x, dividing 3 by 2 gives us a quotient of 1 and a remainder of 1. So, (3/2)x can be expressed as 1 and 1/2x.
For 1/2, dividing 1 by 2 gives us a quotient of 0 and a remainder of 1. So, 1/2 can be expressed as 0 and 1/2.
Therefore, (3/2)x + 1/2 in mixed number form is 1 and 1/2x + 0 and 1/2.
This can also be written as 1 + 1/2x + 0 + 1/2.
So, the final mixed number form is 1 + 1/2x.
To simplify the expression, you need to apply the distributive property and combine like terms.
Step 1: Distribute the fractions:
1/2 (x + 4) + 1/4 (4x - 2)
= (1/2 * x) + (1/2 * 4) + (1/4 * 4x) - (1/4 * 2)
= (1/2 * x) + 2 + (1 * x) - (1/2)
= 1/2 x + 2 + 4x - 1/2
Step 2: Combine like terms:
(1/2 x) + 2 + (4x) - (1/2)
= (1/2 x + 4x) + (2 - 1/2)
= (9/2 x) + (3/2)
Therefore, 1/2 (x + 4) + 1/4 (4x - 2) simplifies to (9/2 x) + (3/2).
To simplify the expression 1/2 (x + 4) + 1/4 (4x - 2), we can first distribute the fractions to the terms inside the parentheses.
Distributing 1/2 to (x + 4), we have (1/2) * x + (1/2) * 4 which simplifies to (1/2)x + 2.
Similarly, distributing 1/4 to (4x - 2), we have (1/4) * 4x + (1/4) * (-2) which simplifies to x - 1/2.
Now, the expression becomes (1/2)x + 2 + x - 1/2.
To combine similar terms, we add the coefficients of x and the constants separately.
2 and -1/2 can be combined as a common fraction by finding the least common denominator, which is 2. Multiplying 2 by 2 gives 4, so -1/2 becomes -2/4.
Now the expression becomes (1/2)x + x + 2 - 2/4.
Combining like terms, we have (1/2 + 1)x + (2 - 2/4), which simplifies to (3/2)x + (8/4 - 2/4), and further simplifies to (3/2)x + 6/4.
To simplify further, we can reduce the fractions. 6/4 simplifies to 3/2, so the final simplified expression is:
(3/2)x + (3/2).
Therefore, the simplified expression for 1/2 (x + 4) + 1/4 (4x - 2) is (3/2)x + (3/2).