Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.(1 po
To add the fractions, first simplify each term:
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2/2 = 1/2x + 1
1/4(4x−2) = 1/4 * 4x - 1/4 * 2 = 1x - 1/2 = x - 1/2
Now, add the two simplified terms together:
1/2x + 1 + x - 1/2
Combine like terms:
1/2x + x + 1 - 1/2
Simplify further:
3/2x + 1/2
The answer in mixed number form would be 1 1/2x.
that's wrong
Apologies for the mistake. Let's solve it again.
To add the fractions, first simplify each term:
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2/2 = 1/2x + 1
1/4(4x−2) = 1/4 * 4x - 1/4 * 2 = x - 1/2
Now, add the two simplified terms together:
1/2x + 1 + x - 1/2
Combine like terms:
1/2x + x + 1 - 1/2
Simplify further:
3/2 + 1/2x
The answer in mixed number form would be 1 1/2x.
To add the fractions (1/2)(x+4) and (1/4)(4x-2), we need to find a common denominator for both fractions. In this case, the common denominator is 4.
First, let's multiply the numerator and denominator of (1/2) by 2 to get (2/4)(x+4):
(2/4)(x+4) = (2x+8)/4
Next, let's multiply the numerator and denominator of (1/4) by 4 to get (1/4)(4x-2):
(1/4)(4x-2) = (4x-2)/4
Now, we can add the two fractions together:
(2x+8)/4 + (4x-2)/4
To add the fractions, we add the numerators and keep the denominator the same:
(2x+8 + 4x-2)/4
Simplifying the numerator by combining like terms:
(6x+6)/4
To express the answer in mixed number form, we divide the numerator by the denominator and write the quotient with the remainder over the original denominator:
(6x+6)/4 = (6x/4) + (6/4) = 1 2/4
Simplifying the fraction:
1 2/4 = 1 1/2
Therefore, the final answer in mixed number form is 1 1/2.
To add the given expression, 1/2(x + 4) + 1/4(4x - 2), we can follow these steps:
Step 1: Distribute the fractions
Using the distributive property, distribute the fractions across the parentheses.
(1/2) * (x + 4) + (1/4) * (4x - 2)
Simplifying each term, we get:
(1/2)x + (1/2) * 4 + (1/4) * 4x - (1/4) * 2
Step 2: Simplify the expressions within the parentheses
(1/2)x + (1/2) * 4 + (1/4) * 4x - (1/4) * 2
= (1/2)x + 2 + x - 1/2
Step 3: Combine like terms
Combine the terms having the same variable.
(1/2)x + x + 2 - 1/2
Adding the x terms,
(3/2)x + 2 - 1/2
Step 4: Simplify the constants
2 - 1/2 can be expressed as a mixed number.
2 - 1/2 = 1 1/2
Step 5: Combine the variable term and the constant term
(3/2)x + 1 1/2
Therefore, the sum of the given expression in mixed number form is (3/2)x + 1 1/2.