1/2(3/5x-8)+7/4(2/5x+4) Simplified

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Jun 16, 2024

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Simplifying the Expression: 1/2(3/5x-8)+7/4(2/5x+4)

In this article, we will simplify the algebraic expression 1/2(3/5x-8)+7/4(2/5x+4). To do this, we will follow the order of operations (PEMDAS) and combine like terms.

Step 1: Expand the Brackets

First, let's expand the brackets by multiplying the terms inside the parentheses with the fractions outside:

1/2(3/5x-8) = 1/2(3/5x) - 1/2(8) = 3/10x - 4

7/4(2/5x+4) = 7/4(2/5x) + 7/4(4) = 7/10x + 7

Step 2: Combine Like Terms

Now, let's combine the like terms:

3/10x - 4 + 7/10x + 7

Step 3: Simplify the Expression

Combine the x terms:

(3/10 + 7/10)x = 10/10x = x

Add the constants:

-4 + 7 = 3

So, the simplified expression is:

x + 3

Therefore, the simplified form of the expression 1/2(3/5x-8)+7/4(2/5x+4) is x + 3.