Evaluating Algebraic Expressions: 5x - (9x + 14) and 3(x + 10) - 2
In this article, we will evaluate two algebraic expressions: 5x - (9x + 14) and 3(x + 10) - 2. These expressions involve variables, constants, and algebraic operations, and we will use the order of operations (PEMDAS) to simplify them.
Expression 1: 5x - (9x + 14)
To evaluate this expression, we need to follow the order of operations:
- Evaluate the expression inside the parentheses: 9x + 14
- Subtract the result from 5x
Let's start by evaluating the expression inside the parentheses:
9x + 14 = 9x + 14
Now, we subtract the result from 5x:
5x - (9x + 14) = 5x - 9x - 14 = -4x - 14
So, the simplified expression is -4x - 14.
Expression 2: 3(x + 10) - 2
To evaluate this expression, we need to follow the order of operations:
- Evaluate the expression inside the parentheses: x + 10
- Multiply the result by 3
- Subtract 2 from the result
Let's start by evaluating the expression inside the parentheses:
x + 10 = x + 10
Now, we multiply the result by 3:
3(x + 10) = 3x + 30
Finally, we subtract 2 from the result:
3x + 30 - 2 = 3x + 28
So, the simplified expression is 3x + 28.
Conclusion
In this article, we evaluated two algebraic expressions: 5x - (9x + 14) and 3(x + 10) - 2. By following the order of operations and applying the correct algebraic operations, we were able to simplify the expressions to -4x - 14 and 3x + 28, respectively.
