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Chapter 5: Problem 57

Simplify it by combining any like terms. $$ 4.7 x+8.3=-5.8 $$

Short Answer

Expert verified
The equation simplifies to \(4.7x = -14.1\).

Step by step solution

01

Identify Like Terms

Look at the expression on the left side: \(4.7x + 8.3\). Notice that \(4.7x\) is the term with the variable \(x\) and \(8.3\) is a constant. There are no like terms to combine together on the left.
02

Isolate the Term with Variable

Subtract \(8.3\) from both sides of the equation to isolate the term with the variable.\[4.7x + 8.3 - 8.3 = -5.8 - 8.3 \ 4.7x = -14.1\]
03

Simplify the Variable Term

Now that you have \(4.7x = -14.1\), the expression is simplified in terms of isolating \(4.7x\). There are no more like terms to combine.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Like Terms
In the realm of prealgebra equations, **like terms** are terms that contain the same variables raised to the same power. This concept is crucial for simplifying mathematical expressions. For instance, in the expression \(4.7x + 8.3\), the term \(4.7x\) has the variable \(x\), whereas \(8.3\) is a constant term with no variables. Like terms must share both the same variable and power. Here:
  • \(4.7x\) stands alone as it is the only term with the variable \(x\).
  • \(8.3\) is a constant and does not pair with \(4.7x\) since constants are not similar to variable terms in this context.
When simplifying, search the entire equation to ensure all possible like terms have been combined. If you cannot find any, move to the next step in solving your equation. This helps streamline the equation-solving process.
Isolating the Variable
To solve equations efficiently, it is often necessary to **isolate the variable**. This means manipulating the equation until the variable appears on one side of the equation, and the constants (numbers) are on the other side. Consider the equation \(4.7x + 8.3 = -5.8\). Here鈥檚 how you isolate the variable:
  • Begin by getting rid of the constant on the same side as the variable. You can do this by doing the opposite mathematical operation. Here, subtract \(8.3\) from both sides of the equation.
  • This results in \(4.7x + 8.3 - 8.3 = -5.8 - 8.3\), which simplifies to \(4.7x = -14.1\).
Isolating the variable is crucial because it sets the stage for solving the equation completely, making it easier to understand and solve for the unknown quantity.
Simplifying Expressions
**Simplifying expressions** involves making a mathematical expression easier to interpret by performing all possible operations. In our example, we tackled the equation \(4.7x + 8.3 = -5.8\) to simplify the expression for easier interpretation.
  • After isolating the variable, as we've done previously, you are left with \(4.7x = -14.1\).
  • These steps ensure the expression is as straightforward as possible besides solving for \(x\). For further simplicity, dividing both sides by \(4.7\) would give you the final value of \(x\).
Simplification leverages basic arithmetic operations and is an essential skill in algebra, as it makes solving complex equations much more manageable and helps uncover the solution efficiently.

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