Unit 4 lesson 6 math

Question

Add and subtract algebraic expressions
1/2(x + 4) + 1/4 (4x-2)

Answer 1

To solve this expression, we will distribute the coefficients to each term inside the parentheses, and then combine like terms.

First, let's distribute 1/2 to (x + 4):
1/2(x + 4) = 1/2 * x + 1/2 * 4
= 1/2x + 2

Next, let's distribute 1/4 to (4x - 2):
1/4(4x - 2) = 1/4 * 4x - 1/4 * 2
= x - 1/2

Now, we can combine the like terms:
1/2(x + 4) + 1/4(4x - 2) = (1/2x + 2) + (x - 1/2)

To add these two expressions, we need to find a common denominator for the fractions, which in this case is 2:
(1/2x + 2) + (x - 1/2) = (1/2x + 2) + (2/2x - 1/2)
= (1/2x + 2/2x) + (2 - 1/2)
= (3/2x) + (3/2)

Since both terms have the same denominator, we can combine them:
(3/2x) + (3/2) = (3/2x + 3/2)

Therefore, the simplified expression is 3/2x + 3/2.