Simplifying Algebraic Expressions: 3/2x+3x-3/2x-1+2x^2+1/4x^2-2x
In this article, we will simplify the algebraic expression 3/2x+3x-3/2x-1+2x^2+1/4x^2-2x. To do so, we will follow the order of operations (PEMDAS) and combine like terms.
Step 1: Combine Like Terms with the Same Variable
First, let's focus on the terms with the variable x:
- 3/2x + 3x - 3/2x = ? To combine these terms, we need to find a common denominator, which is 2. Then, we can add and subtract the terms:
(3/2)x + 3x - (3/2)x = (3/2)x + (6/2)x - (3/2)x = (6/2)x = 3x
Now, the expression becomes:
3x - 1 + 2x^2 + 1/4x^2 - 2x
Step 2: Combine Like Terms with the Same Variable (Again!)
Next, let's focus on the terms with the variable x^2:
- 2x^2 + 1/4x^2 = ? To combine these terms, we need to find a common denominator, which is 4. Then, we can add the terms:
2x^2 + (1/4)x^2 = 2x^2 + (1/4)x^2 = (9/4)x^2
Now, the expression becomes:
3x - 1 + (9/4)x^2 - 2x
Step 3: Combine Like Terms (Final Step!)
Finally, let's combine the remaining terms:
- 3x - 2x = x
- -1 remains as it is
Now, we can write the simplified expression:
(9/4)x^2 + x - 1
And that's the final answer! We have successfully simplified the algebraic expression 3/2x+3x-3/2x-1+2x^2+1/4x^2-2x.
