(- 5/6 * X - 7/12) - (- 1/3 * X - 1/4)

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Jun 07, 2024

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Simplifying Algebraic Expressions: (- 5/6 * x - 7/12) - (- 1/3 * x - 1/4)

In this article, we will explore how to simplify the algebraic expression (- 5/6 * x - 7/12) - (- 1/3 * x - 1/4). Simplifying algebraic expressions involves combining like terms and eliminating any parentheses or negative signs.

Step 1: Distribute the Negative Sign

To begin, we need to distribute the negative sign to the terms inside the parentheses:

- (- 1/3 * x - 1/4) = 1/3 * x + 1/4

So, the expression becomes:

(- 5/6 * x - 7/12) + (1/3 * x + 1/4)

Step 2: Combine Like Terms

Next, we need to combine like terms. In this case, we have two terms with x and two constant terms.

- 5/6 * x + 1/3 * x = (- 5/6 + 1/3) * x

To add these fractions, we need a common denominator, which is 12. So, we can rewrite the fractions as:

- 10/12 * x + 4/12 * x = - 6/12 * x = - 1/2 * x

Now, let's combine the constant terms:

- 7/12 + 1/4 = - 7/12 + 3/12 = - 4/12 = - 1/3

Step 3: Write the Simplified Expression

So, the simplified expression is:

- 1/2 * x - 1/3

And that's it! We have successfully simplified the algebraic expression (- 5/6 * x - 7/12) - (- 1/3 * x - 1/4).