Simplifying Algebraic Expressions: 2-3(1-2x) = 5-2(2x+3)
In this article, we will explore how to simplify the algebraic expression 2-3(1-2x) = 5-2(2x+3). This expression involves variables, constants, and algebraic operations, which can be simplified using the rules of algebra.
Step 1: Evaluate the Expression 2-3(1-2x)
To simplify the expression 2-3(1-2x), we need to follow the order of operations (PEMDAS):
- Evaluate the expression inside the parentheses: 1-2x
- Multiply the result by -3: -3(1-2x) = -3 + 6x
- Add 2 to the result: 2 - 3 + 6x = -1 + 6x
So, the simplified expression is -1 + 6x.
Step 2: Evaluate the Expression 5-2(2x+3)
To simplify the expression 5-2(2x+3), we need to follow the order of operations (PEMDAS):
- Evaluate the expression inside the parentheses: 2x+3
- Multiply the result by -2: -2(2x+3) = -4x - 6
- Add 5 to the result: 5 - 4x - 6 = -1 - 4x
So, the simplified expression is -1 - 4x.
Comparing the Two Expressions
Now that we have simplified both expressions, we can compare them:
-1 + 6x = -1 - 4x
To solve for x, we can add 1 to both sides of the equation:
6x = -4x
Next, we can add 4x to both sides of the equation:
10x = 0
Finally, we can divide both sides of the equation by 10:
x = 0
Therefore, the value of x that satisfies the equation is x = 0.
Conclusion
In this article, we have simplified the algebraic expression 2-3(1-2x) = 5-2(2x+3) and solved for x. By following the rules of algebra and the order of operations, we were able to simplify the expression and find the value of x that satisfies the equation.
