Problem 63 - Elementary Algebra Within Reach

Question

Solve the equation. Round your answer to two decimal places. $$\frac{x}{3.155}=2.850$$

Step-by-Step Solution

Answer

The solution to the equation is \(x = 8.99\) when rounded to two decimal places.

Step 1: Identify the Given Equation

The given equation is \(\frac{x}{3.155} = 2.850\). The goal is to solve for the unknown variable \(x\).

Step 2: Apply Basic Algebraic Operations

To isolate \(x\), multiply both sides of the equation by \(3.155\). This gives\(x = 3.155 * 2.850\).

Step 3: Result

Calculate the value of \(x\). You get \(x= 8.99175\).

Key Concepts

Basic Algebraic Operations

Basic algebraic operations are the building blocks of algebra. They include addition, subtraction, multiplication, and division. These operations are used to manipulate equations, which helps you find the value of unknown variables. In the original exercise, basic algebraic operations were applied to solve the given equation \(\frac{x}{3.155} = 2.850\). Here are some key steps on how these operations were utilized:\

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• Identify the Operation: Since \(x\) is divided by \(3.155\), we can use multiplication to cancel the division.
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• Applying Multiplication: Multiply both sides by \(3.155\) to isolate \(x\).
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• Simplifying: The equation changes to \(x = 3.155 \times 2.850\).
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\These fundamental operations assist in reshaping equations, allowing you to solve for the unknown and progress toward the solution.

Solving Equations

Solving equations is about finding the value of the unknown variable that makes the equation true. In this problem, the task is to find what values of \(x\) satisfy the equation. Here’s a closer look at the process:\

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• Isolating the Variable: The goal is to have \(x\) on one side of the equation by itself. By multiplying both sides by \(3.155\), the division cancels out, leaving \(x = 3.155 \times 2.850\).
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• Calculating the Solution: Perform the multiplication to find \(x\). Here, multiplying \(2.850\) by \(3.155\) yields \(x = 8.99175\).
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\Always double-check your calculations and ensure that each step logically follows the previous one. The correct application of algebraic rules will guide you to the accurate solution.

Rounding Numbers

Rounding numbers helps to make calculations and results easier to read and understand, especially when precision is not crucial. In this exercise, the result \(x = 8.99175\) is rounded to two decimal places. Here's how you can round numbers effectively:\

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• Identify the Decimal Place: Look at the third decimal place to decide whether to round up or stay. If it's 5 or more, round up.
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• Applying Rounding: With \(8.99175\), examine the third decimal place (1). Since it's less than 5, you round down, keeping the number as \(8.99\).
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• Verification: Ensure the final rounded number makes sense given the context of the problem.
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\Rounding helps to provide a more user-friendly answer that avoids unnecessary complexity, while still retaining the necessary accuracy for most practical purposes.