Simplifying the Expression: 3/4x - 1/3 + 7/8x - 1/2
In this article, we will simplify the algebraic expression: 3/4x - 1/3 + 7/8x - 1/2.
Step 1: Combine Like Terms
First, let's combine the terms with the variable x:
3/4x + 7/8x
To add these fractions, we need a common denominator, which is the least common multiple (LCM) of 4 and 8, which is 8. So, we can rewrite the fractions with a denominator of 8:
6/8x + 7/8x
Now, we can add them:
13/8x
Step 2: Simplify the Constant Terms
Next, let's simplify the constant terms:
-1/3 - 1/2
To subtract these fractions, we need a common denominator, which is the LCM of 3 and 2, which is 6. So, we can rewrite the fractions with a denominator of 6:
-2/6 - 3/6
Now, we can subtract them:
-5/6
Step 3: Combine the Results
Finally, let's combine the results from Steps 1 and 2:
13/8x - 5/6
And that's the simplified expression!
Final Answer: 13/8x - 5/6
