Add: 1/2( x + 4) + 1/4 (4x - 2). Answer should be in mixed number form.
To simplify the expression, let's simplify each term separately:
1/2 (x + 4) = 1/2x + 1/2(4) = 1/2x + 2
1/4 (4x - 2) = 1/4(4x) - 1/4(2) = x - 1/2
Now let's add the two simplified terms:
1/2x + 2 + x - 1/2 = 3/2x + 2 - 1/2
The denominators of 2 and 1/2 are different, so we need to find a common denominator. The least common multiple of 2 and 1/2 is 2.
So, we multiply each term by 2 to get a common denominator:
(3/2x)⋅2 + 2⋅2 - (1/2)⋅2
= 3x + 4 - 1
= 3x + 3
Therefore, 1/2( x + 4) + 1/4 (4x - 2) simplified to mixed number form is 3x + 3.
It said it was incorrect..
I apologize for the confusion. Let's try again:
1/2 (x + 4) = 1/2 * x + 1/2 * 4 = 1/2x + 2
1/4 (4x - 2) = 1/4 * 4x - 1/4 * 2 = x - 1/2
Now let's add the two simplified terms:
(1/2x + 2) + (x - 1/2) = 1/2x + x + 2 - 1/2
Combine like terms:
1/2x + x + 2 - 1/2 = (1/2x + x) + (2 - 1/2) = 3/2x + 3/2
To convert this to mixed number form, we divide the numerator (3) by the denominator (2):
3 divided by 2 is 1 with a remainder of 1
So, we have 1 and 1/2.
Therefore, 1/2( x + 4) + 1/4 (4x - 2) simplified to mixed number form is 1 1/2.
Still said incorrect ;(
I apologize for the confusion. Let's try solving it again:
1/2(x + 4) + 1/4(4x - 2)
Distribute the fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
1/2x + 2/2 + 4/4x - 2/4
Simplify the fractions:
1/2x + 1 + x - 1/2
Combine like terms:
1/2x + x + 1 - 1/2
3/2x + 1/2
Now, let's convert this to mixed number form:
The whole number part is obtained by dividing the numerator (3) by the denominator (2):
3 divided by 2 is 1 with a remainder of 1
So, the whole number part is 1.
The fractional part is 1/2.
Therefore, the final answer is 1 1/2.
Add: 1/2 (x + 4) + 1/4 (4x - 2). Answer should be in mixed number form.
Apologies for the confusion. Let's solve it again:
1/2(x + 4) + 1/4(4x - 2)
Distribute the fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
1/2x + 2/2 + 1x - 1/2
Simplify the fractions:
1/2x + 1 + 1x - 1/2
Combine like terms:
1/2x + 1x + 1 - 1/2
Adding the coefficients of x:
(1/2 + 1) x + 1 - 1/2
3/2 x + 1 - 1/2
Now, to convert it to a mixed number, let's find a common denominator for 2 and 1/2, which is 2.
(3/2 x) - (1/2)
3x/2 - 1/2
Now, let's simplify:
3x - 1/2
As a mixed number, it can be written as:
2 1/2x - 1/2
Therefore, the answer in mixed number form is 2 1/2x - 1/2.
Wrong
Apologies for the mistake. Let's solve it again:
1/2(x + 4) + 1/4(4x - 2)
Distribute the fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
1/2x + 2/2 + x - 1/2
Simplify the fractions:
1/2x + 1 + x - 1/2
Combine like terms:
(1/2x + x) + (1 - 1/2)
3/2x + 1/2
Now, let's convert it to a mixed number:
The whole number part is obtained by dividing the numerator (3) by the denominator (2):
3 divided by 2 is 1 with a remainder of 1
So, the whole number part is 1.
The fractional part is 1/2.
Therefore, the answer in mixed number form is 1 1/2x + 1/2.
To solve the given expression: 1/2(x + 4) + 1/4(4x - 2) and express it in mixed number form, we can follow these steps:
Step 1: Distribute the fractions to eliminate parentheses:
1/2(x + 4) + 1/4(4x - 2)
= (1/2)(x) + (1/2)(4) + (1/4)(4x) - (1/4)(2)
Step 2: Simplify each term:
= (1/2)x + 2/2 + (4/4)x - 2/4
Step 3: Combine like terms:
= (1/2)x + x + 2 - 1/2
Step 4: Convert all fractions to have a common denominator:
= (2/4)x + (4/4)x + 2 - (2/4)
= (6/4)x + 2 - (2/4)
Step 5: Simplify the mixed number:
= (6/4)x + 2 - (2/4)
= (6/4)x + 2 - 1/2
Step 6: Convert the improper fraction to a mixed number:
= (3/2)x + 1 1/2
So, the expression 1/2(x + 4) + 1/4(4x - 2) in mixed number form is (3/2)x + 1 1/2.