1/2 (x + 4) + 1/4(4x - 2)
To simplify the expression 1/2 (x + 4) + 1/4(4x - 2), we need to distribute the coefficients.
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 like terms:
1/2x + 2 + x - 1/2
Combining like terms means adding or subtracting the coefficients of the same variables.
So, 1/2x + x = (1/2 + 2/2)x = 3/2x
And 2 - 1/2 = 4/2 - 1/2 = 3/2
Therefore, the simplified expression is 3/2x + 3/2 or in standard form, (3/2)x + 3/2.
To simplify the expression 1/2 (x + 4) + 1/4 (4x - 2), you need to distribute the fractions and then combine like terms.
Step 1: Distribute the first fraction:
1/2 (x + 4) = 1/2 * x + 1/2 * 4 = 1/2 * x + 2
Step 2: Distribute the second fraction:
1/4 (4x - 2) = 1/4 * 4x + 1/4 * -2 = x - 1/2
Step 3: Combine like terms:
1/2 * x + 2 + x - 1/2
Combine the x terms:
1/2x + x = 3/2x
Combine the constant terms:
2 - 1/2 = 3/2
Putting it all together:
3/2x + 3/2 = (3/2)x + (3/2)
To simplify the expression 1/2 (x + 4) + 1/4(4x - 2), we can follow these steps:
Step 1: Distribute the 1/2 to the terms inside the first parentheses.
1/2 (x + 4) becomes 1/2 * x + 1/2 * 4, which simplifies to 1/2 x + 2.
Step 2: Distribute the 1/4 to the terms inside the second parentheses.
1/4 (4x - 2) becomes 1/4 * 4x + 1/4 * (-2), which simplifies to x - 1/2.
Now we can combine the like terms:
(1/2 x + 2) + (x - 1/2)
Step 3: Group the x terms together and the constant terms together.
(1/2 x + x) + (2 - 1/2)
Step 4: Combine the x terms and the constant terms separately.
(3/2 x) + (3/2)
So, the simplified expression is 3/2 x + 3/2.