Simplifying the Expression: 1/4x + 1 + 3/4x - 2/3 - 1/2x
In this article, we will simplify the algebraic expression: 1/4x + 1 + 3/4x - 2/3 - 1/2x.
Step 1: Combine like terms
First, let's combine the terms with the variable x.
1/4x + 3/4x - 1/2x
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 4, 4, and 2 is 4. So, we can rewrite each fraction with a denominator of 4:
(1/4)x + (3/4)x - (2/4)x
Now, we can add and subtract the fractions:
(1 + 3 - 2)/4x = 2/4x = 1/2x
So, the simplified expression with x is 1/2x.
Step 2: Simplify the constant terms
Next, let's simplify the constant terms:
1 - 2/3
We can rewrite the fraction with a denominator of 3:
1 - (2/3)
To subtract a fraction from a whole number, we can convert the whole number to an equivalent fraction with the same denominator:
(3/3) - (2/3) = 1/3
So, the simplified constant term is 1/3.
Final Answer
Now, we can combine the simplified expressions with x and the constant term:
1/2x + 1/3
Therefore, the simplified expression is 1/2x + 1/3.
