Add: 1/2(x+4)+1/4(4x-2)
To simplify the expression, we need to first distribute the fractions into the parentheses.
1/2(x + 4) + 1/4(4x - 2)
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + 4/4x - 2/4
= 1/2x + 1 + x - 1/2
= 1/2x + x + 1 - 1/2
= (1/2x + x) + (1 - 1/2)
= (3/2x) + (1/2)
So, 1/2(x + 4) + 1/4(4x - 2) simplifies to (3/2x) + (1/2).
To add the given expression, we need to combine like terms.
First, let's simplify the expression inside the parentheses:
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, we can combine the two simplified expressions:
1/2x + 2 + x - 1/2
Next, we need to add the coefficients of the x terms and the constant terms separately:
(1/2x + x) + (2 - 1/2)
Simplifying:
(1/2 + 1)x + (2 - 1/2)
Now, we can add the fractions:
(3/2)x + (3/2)
Therefore, the final simplified expression is:
(3/2)x + (3/2)
To add the given expression 1/2(x+4) + 1/4(4x-2), we need to simplify it step-by-step.
Step 1: Distribute the fractions
1/2(x+4) + 1/4(4x-2) becomes 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Step 2: Simplify the multiplication of fractions
1/2 * x simplifies to x/2
1/2 * 4 simplifies to 4/2, which simplifies further to 2
1/4 * 4x simplifies to 4x/4, which simplifies further to just x
1/4 * -2 simplifies to -2/4, which simplifies further to -1/2
Step 3: Combine like terms
Now let's combine the like terms:
x/2 + 2 + x - 1/2
Step 4: Simplify by combining similar terms
x/2 and x can be combined since they have the same variable:
x/2 + x = 3x/2
So the simplified expression 1/2(x+4) + 1/4(4x-2) becomes:
3x/2 + 2 - 1/2
Step 5: Combine the last two terms
2 - 1/2 can be simplified by finding a common denominator:
2 = 4/2
Combining with -1/2, we get 4/2 - 1/2 = 3/2
Therefore, the final simplified expression is:
3x/2 + 3/2 or (3x + 3)/2