91Ó°ÊÓ

When simplifying algebraic expressions, a crucial step is combining like terms. Like terms are terms that have the same variable raised to the same power. For example, in the expression \(0.8x - 5 - x + 2.7\), \(0.8x\) and \(-x\) are like terms because they both contain the variable \(x\), while \(-5\) and \(2.7\) are constants and can be combined.

To combine like terms, add or subtract their coefficients. For instance, combining \(0.8x\) and \(-x\) involves subtracting 1 from 0.8, resulting in \(-0.2x\). Similarly, combine \(-5\) and \(+2.7\) by adding them to get \(-2.3\).

Following these steps allows us to simplify the expression step by step, ultimately making complex problems easier to solve.

Variable terms are parts of algebraic expressions that contain variables, such as \(x\) or \(y\). In our example, the variable terms are \(0.8x\) and \(-x\). These terms are essential because they represent numbers that can change depending on the value of the variable.

When simplifying, it is important to handle variable terms properly by combining their coefficients. Remember that if no coefficient is visible (e.g., \(-x\)), it is implicitly 1 or \(-1\).

By focusing on the coefficients, you can combine variable terms easily. In our example, we combined \(0.8x\) and \(-x\) to get \(-0.2x\), simplifying the expression considerably.

Constant terms are the numbers in an expression without a variable, like \(-5\) and \(+2.7\) in the example \(0.8x - 5 - x + 2.7\). Constants do not change because they aren’t affected by the variables in the expression.

To simplify expressions, group together all constant terms and perform the relevant operations, such as addition or subtraction. For instance, adding \(-5\) and \(+2.7\) yields \(-2.3\).

Proper handling of constant terms makes the overall process of simplifying expressions much more straightforward and ensures clarity in your final answer.