Simplify the expression:
1.75x−2
The Correct Answer and Explanation is:
To simplify the expression (1.75x – 2), we first need to analyze the components of the expression. The expression consists of two terms: (1.75x) and (-2). Here’s a step-by-step breakdown of the simplification process:
- Identify the Terms: The expression is composed of a variable term (1.75x) and a constant term (-2). The variable term involves the variable (x), while the constant term is simply a numerical value.
- Understanding the Structure: The expression is already in its simplest form in terms of combining like terms. Like terms are terms that have the same variable raised to the same power. In this case, (1.75x) and (-2) are not like terms, as one involves the variable (x) and the other does not. Therefore, we cannot combine them further.
- Checking for Common Factors: There are no common factors between the terms (1.75x) and (-2) that can be factored out. Factoring would typically involve finding a number that can divide both terms evenly, but since they are not similar in nature, this step does not apply here.
- Final Expression: Since there are no like terms to combine or factors to simplify further, the expression remains as is. Thus, the simplified expression of (1.75x – 2) is simply (1.75x – 2).
- Interpretation: In practical terms, (1.75x – 2) represents a linear expression where the coefficient of (x) is (1.75), indicating the rate of change in relation to (x), and (-2) represents a constant that shifts the graph of the linear equation downward on the y-axis.
In conclusion, the expression (1.75x – 2) is already in its simplest form, meaning no further simplification is necessary, and it effectively communicates a linear relationship between the variable (x) and the constant.