1/9(3x+7)-1/3(x+2)

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Jun 16, 2024

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Simplifying Algebraic Expressions: 1/9(3x+7) - 1/3(x+2)

In this article, we will explore the simplification of the algebraic expression 1/9(3x+7) - 1/3(x+2).

Step 1: Distribute the Fractions

To simplify the expression, we need to distribute the fractions to the terms inside the parentheses.

1/9(3x + 7) = 1/9(3x) + 1/9(7) = 3x/9 + 7/9 1/3(x + 2) = 1/3(x) + 1/3(2) = x/3 + 2/3

Step 2: Rewrite the Expression

Now, let's rewrite the original expression using the distributed fractions:

1/9(3x+7) - 1/3(x+2) = (3x/9 + 7/9) - (x/3 + 2/3)

Step 3: Combine Like Terms

Next, we need to combine like terms:

3x/9 - x/3 = 3x/9 - 3x/9 = 0 (since 3x/9 and x/3 are equivalent fractions) 7/9 - 2/3 = 7/9 - 6/9 = 1/9 (since 2/3 = 6/9)

Step 4: Simplify the Expression

Finally, we can simplify the expression:

1/9(3x+7) - 1/3(x+2) = 0 + 1/9 = 1/9

Therefore, the simplified form of the algebraic expression 1/9(3x+7) - 1/3(x+2) is 1/9.