Problem 57 - Beginning and Intermediate Algebra

Question

Simplify each expression. \(2.3 x-1.1+4.2 x-0.7\)

Step-by-Step Solution

Answer

6.5x - 1.8

Step 1: Combine Like Terms

Identify and group the like terms in the expression. Here, the terms involving x are like terms: \(2.3x\) and \(4.2x\). The constant terms \(-1.1\) and \(-0.7\) are also like terms.

Step 2: Add the Coefficients of x

Add the coefficients of the x terms: \(2.3 + 4.2\). This gives \(6.5x\).

Step 3: Add the Constant Terms

Add the constant terms: \(-1.1 + (-0.7)\). This gives \(-1.8\).

Step 4: Write the Simplified Expression

Combine the simplified x term and the constant term to write the final simplified expression. This gives: \(6.5x - 1.8\).

Key Concepts

Combining Like Terms

In algebra, one of the first steps to simplify an expression is combining like terms.
Like terms are terms that have the same variable raised to the same power.
For example, in the expression from our exercise, we have:

• Terms involving x: \(2.3x\) and \(4.2x\)
• Constant terms: \(-1.1\) and \(-0.7\)

To combine like terms, you simply add or subtract their coefficients.
This makes the expression simpler and easier to work with. When you combine, make sure you are only combining terms that are alike.

Coefficients

A coefficient is a number that multiplies a variable.
It's the numerical part of a term that contains a variable.
In our given exercise, the coefficients are \(2.3\) and \(4.2\).
When combining like terms, you add the coefficients together.
Here’s how you do it with our exercise:
- Add the coefficients of the x terms: \(2.3x + 4.2x\)
- This results in \(6.5x\).
Understanding coefficients helps simplify expressions and solve equations more easily.

Constants

Constants are numbers without variables.
They remain the same, no matter what the variables equal.
In our exercise, the constants are \(-1.1\) and \(-0.7\).
To combine these constants, you perform the necessary arithmetic:

• Add the constants: \(-1.1 + (-0.7) = -1.8\)

Combining constants is as straightforward as basic addition and subtraction, and it helps simplify the overall expression.
By combining the constant terms, we ensure the expression is as simplified as possible, making it easier to understand and solve.