Problem 11 - Algebra A Combined Function

Question

Simplify each expression by combining any like terms. $$ 6.2 x-4+x-1.2 $$

Step-by-Step Solution

Answer

The simplified expression is \(7.2x - 5.2\).

Step 1: Identify Like Terms

First, look at the expression to identify like terms. The expression is: \(6.2x - 4 + x - 1.2\). The like terms here are the ones with \(x\) – specifically, \(6.2x\) and \(x\), as well as the constant terms \(-4\) and \(-1.2\).

Step 2: Combine the Like Terms with \(x\)

Add together the coefficients of the \(x\) terms. We have \(6.2x\) and \(x\), which is equivalent to \(1x\). Adding these together gives \((6.2 + 1)x = 7.2x\).

Step 3: Combine the Constant Terms

Now, combine the constant terms \(-4\) and \(-1.2\). Adding these gives \(-4 + (-1.2) = -5.2\).

Step 4: Write the Simplified Expression

Combine the results from the previous steps to form the simplified expression: \(7.2x - 5.2\).

Key Concepts

Like Terms in Algebra

In algebra, like terms are terms that have the same variable raised to the same power. Only their coefficients are different. Identifying like terms is a critical first step in simplifying expressions, as it allows us to combine them effectively. For example, consider the expression \(6.2x - 4 + x - 1.2\).

• The terms \(6.2x\) and \(x\) are like terms because they both contain the variable \(x\).
• On the other hand, \(-4\) and \(-1.2\) are like terms because they are constants, which are terms without a variable.

By identifying which terms are alike, we can group them together and simplify the problem more easily.

Combining Coefficients

Once like terms have been identified, the next step in simplifying an algebraic expression is to combine their coefficients. Coefficients are the numbers that multiply the variables in an expression. To combine the coefficients, simply perform the appropriate arithmetic operation. Let’s look at our example:

In the expression, \(6.2x\) and \(x\) are like terms. Here, the coefficient of \(6.2x\) is \(6.2\), and the coefficient of \(x\) is an understood \(1\). Simply add these coefficients together:

• \(6.2 + 1 = 7.2\)

Thus, combining these gives you \(7.2x\). This simplifies the expression by reducing the number of terms and makes further calculations easier.

Constants in Algebra Expressions

Constants in algebra are numbers without any variables attached. They stand alone and, like other terms, can be combined when simplifying expressions. In our example, the constants \(-4\) and \(-1.2\) are considered like terms.

To combine constants, simply add or subtract them as indicated in the expression:

• For \(-4\) and \(-1.2\), you perform the calculation: \(-4 + (-1.2) = -5.2\).

Once these constants are combined, you can use the result to further simplify the expression. Combining constants helps eliminate clutter in an equation, streamlining it into fewer terms. This is essential for accurately solving or further manipulating algebraic expressions.