Problem 68 Solve. $$ 48,916 \cdot x=14,... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 68

Solve. $$ 48,916 \cdot x=14,332,388 $$

Short Answer

Expert verified

x = 293

Step by step solution

- Understand the Equation

The given equation is $48,916 \times x = 14,332,388$. This is a basic linear equation where the goal is to solve for $x$.

- Isolate the Variable

To find the value of $x$, isolate $x$ by dividing both sides of the equation by $48,916$.

- Perform the Division

Divide $14,332,388$ by $48,916$ to get $x$: \[ x = \frac{14,332,388}{48,916} \] Simplifying this division yields $x = 293$.

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Key Concepts

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

Solving Equations

Solving equations is a fundamental skill in algebra. An equation is a statement that two expressions are equal. In a linear equation like this one, we aim to find the value of the variable that makes the equation true. To do this, we use operations that will help simplify the equation and isolate the variable. It鈥檚 like a puzzle where each piece needs to fit in the correct place! We often encounter equations in the form of $a \cdot x = b$, where the goal is to find the unknown variable, represented as $x$. Here, $a$ and $b$ are constants.

Division

In this exercise, the key operation is division. To isolate the variable $x$, we divide both sides of the equation by the same number. This step is crucial because it simplifies the equation and helps us find the value of $x$. For example, starting with the equation $48,916 \times x = 14,332,388$, we divide each side by $48,916$ to get \[ x = \frac{14,332,388}{48,916} \]. Division helps us break down the problem into smaller, more manageable parts. Once we complete the division, we find that $x = 293$.

Mathematical Isolation

Mathematical isolation involves rearranging an equation to get the variable alone on one side. This is done through inverse operations. In this exercise, our goal was to isolate $x$. We started with $48,916 \times x = 14,332,388$. To isolate $x$, we needed to eliminate the coefficient 48,916 by dividing both sides by it. This left us with $x = \frac{14,332,388}{48,916} = 293$. By isolating the variable, we simplify the equation and make it easier to understand and solve. This skill is fundamental for solving more complex equations and is widely used in algebra and beyond!

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91影视

Solve. $$ 48,916 \cdot x=14,332,388 $$

Short Answer

Step by step solution

- Understand the Equation

- Isolate the Variable

- Perform the Division

Key Concepts

Solving Equations

Division

Mathematical Isolation

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