Add: 1/2(x+4)+1/4(4x−2)
1/2(x+4) + 1/4(4x-2)
First, simplify each fraction by multiplying the numerator and denominator by the least common multiple of the denominators.
For 1/2(x+4):
1/2(x+4) = 1/2 * (x+4) / 1 * 2 = (1/2)x + 2
For 1/4(4x-2):
1/4(4x-2) = 1/4 * (4x-2) / 1 * 4 = (1/4)(4x-2) / 1 = (1/4)(4x) - (1/4)(2) = 1x - 1/2 = x - 1/2
Now, our expression becomes:
(1/2)x + 2 + x - 1/2
Combine like terms:
(1/2)x + x + 2 - 1/2
(3/2)x + 2 - 1/2
(3/2)x + 3/2
Simplifying the expression further, we can multiply both the numerator and denominator by 2 to get rid of the fractions:
2 * (3/2)x + 2 * (3/2)
(6/2)x + 6/2
3x + 3
Therefore, the simplified expression is 3x + 3.
thats not right
Apologies for the incorrect simplification. Let's try again.
1/2(x+4) + 1/4(4x-2)
First, distribute the fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplify each term:
1/2x + 2/2 + 1x - 1/2
Combine like terms:
(1/2x + 1x) + (2/2 - 1/2)
(3/2x) + (1/2)
To simplify, we can multiply each term by 2 to get rid of fractions:
2 * (3/2x) + 2 * (1/2)
3x + 1
Therefore, the simplified expression is 3x + 1.
wrong
Apologies for the misunderstanding. Let's try again.
1/2(x+4) + 1/4(4x-2)
Distribute the fractions:
(1/2)(x) + (1/2)(4) + (1/4)(4x) - (1/4)(2)
Simplify each term:
1/2x + 2/2 + 4/4x - 2/4
Combine like terms:
(1/2x + 4/4x) + (2/2 + 2/4)
Simplify further:
(1/2 + 1)x + (1 + 1/2)
Now, find a common denominator for each fraction:
(1/2 + 2/2)x + (2/2 + 1/2)
Combine the fractions:
(3/2)x + (3/2)
Therefore, the simplified expression is (3/2)x + (3/2).
To simplify the expression 1/2(x + 4) + 1/4(4x - 2), we first need to distribute the fractions to their respective terms within the parentheses.
Let's start with the first fraction, 1/2(x + 4):
1/2(x + 4) = (1/2 * x) + (1/2 * 4)
= (1/2 * x) + 2/2
= (1/2 * x) + 1
Next, let's distribute the second fraction, 1/4(4x - 2):
1/4(4x - 2) = (1/4 * 4x) - (1/4 * 2)
= (1 * x) - (1/2)
= x - 1/2
Now that we have simplified both parts, we can combine them:
(1/2(x + 4)) + (1/4(4x - 2)) = [(1/2 * x) + 1] + [x - 1/2]
Next, we can simplify the expression further by combining like terms:
[(1/2 * x) + 1] + [x - 1/2] = (1/2 * x) + 1 + x - 1/2
= 1/2x + x + 1 - 1/2
To add the x terms together, we need a common denominator for 1/2x and x. The least common multiple (LCM) of 2 and 1 is 2, so we multiply 1/2x by 2/2:
= (1/2 * 2/2)x + x + 1 - 1/2
= 2/4x + x + 1 - 1/2
Now, we can add the x terms since they have the same denominator:
= 2/4x + 4/4x + 1 - 1/2
= (2/4 + 4/4)x + 1 - 1/2
= 6/4x + 1 - 1/2
To add 1 and -1/2, we need to find a common denominator. The LCM of 2 and 4 is 4, so we multiply 1 by 2/2 and -1/2 by 4/4:
= 6/4x + 2/2 - 4/4
= 6/4x + 2/2 - 4/4
= 6/4x + 2/4 - 4/4
= 6/4x - 2/4
Finally, we can simplify the expression by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2:
= (6/2)/(4/2)x - (2/2)/(4/2)
= 3/2x - 1/2
Therefore, the simplified expression is 3/2x - 1/2.