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When simplifying algebraic expressions, the first step is to identify like terms. Like terms have the same variable raised to the same power. For example, in 鈥�0.45x + 1.8 - 0.62x鈥�, the terms 鈥�0.45x鈥� and 鈥�-0.62x鈥� are like terms because they both involve the variable 鈥渪鈥�. On the other hand, the constant term 鈥�1.8鈥� does not have a variable and cannot be combined with the terms involving 鈥渪鈥�.

It's important to remember that only like terms can be combined through addition or subtraction. Recognizing like terms is a crucial step in simplifying any algebraic expression.

To identify like terms, look for the same variable and the same exponent. This concept makes the process of combining terms straightforward and systematic.

Once like terms are identified, the next step is to combine their coefficients. The coefficient is the numerical part of a term that is placed in front of the variable. For instance, in 鈥�0.45x鈥�, the coefficient is 0.45. In the case of 鈥�-0.62x鈥�, the coefficient is -0.62.

To combine these coefficients, simply add or subtract them, depending on their signs. In our example, you subtract the coefficient -0.62 from 0.45: \[0.45x - 0.62x = (0.45 - 0.62)x\]

This results in: \[-0.17x\]

Combining coefficients is essential to simplify the expression. It makes the resulting expression more manageable and easier to understand. Exercise this step carefully by paying attention to the arithmetic involving the coefficients.

The final step in the simplification process is to rewrite the expression in its simplest form. After combining the coefficients of like terms, you will be left with fewer terms. In our example: \[-0.17x + 1.8\]

Here, the like terms were combined into 鈥�-0.17x鈥�, and the constant term 鈥�1.8鈥� remains as is. This is as simplified as the expression can get.

Algebraic simplification is all about making expressions cleaner and easier to manage. By following the steps of identifying like terms and combining their coefficients, you can transform complex expressions into simpler ones.

Practicing these steps consistently improves one鈥檚 ability to handle more complicated algebraic expressions efficiently.