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Chapter 2: Problem 101

Solve each equation. $$x-0.06 x=50,000$$

Short Answer

Expert verified
x 鈮� 53,191.49

Step by step solution

01

Combine like terms

Identify the like terms on the left side of the equation. We have the terms involving x: \(x\) and \(-0.06x\). Combine these terms by factoring out x. This gives us: \[ x - 0.06x = 50,000 \] \[ (1 - 0.06)x = 50,000 \] \[ 0.94x = 50,000 \]
02

Isolate x

To solve for x, we need to isolate it on one side of the equation. This can be achieved by dividing both sides of the equation by 0.94: \[ x = \frac{50,000}{0.94} \]
03

Calculate the solution

Perform the division to find the value of x: \[ x = \frac{50,000}{0.94} \approx 53,191.49 \]

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Key Concepts

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

Combining Like Terms
Combining like terms is an essential step in solving linear equations. Like terms are terms that have the same variable raised to the same power. For instance, in the equation given, we have two like terms on the left side: \( x \) and \( -0.06x \). Both terms involve the variable \( x \).
When combining like terms, you add or subtract the coefficients (the numerical parts) of these terms.
This can be shown as:
  • Identify the like terms: \( x \) and \( -0.06x \)
  • Combine them by combining their coefficients: \( 1x - 0.06x = (1 - 0.06)x = 0.94x \)

This simplification leads us to a more manageable equation that is easier to solve.
Factoring
Factoring is a mathematical process of transforming an expression into a product of simpler expressions. In this problem, we combined like terms by factoring out \( x \). Factoring out means extracting the common factor from the terms. Here, both terms on the left side share the variable \( x \).
We rewrite the equation \( x - 0.06x = 50,000 \) as:
  • Factored form: \((1 - 0.06)x = 50,000 \)

This simplifies our equation and makes it straightforward to solve it by isolating the variable.
Isolating Variable
Isolating the variable involves manipulating the equation to get the variable of interest (usually denoted as \( x \) or another letter) on one side by itself. Once we have the simplified equation \( 0.94x = 50,000 \), the next step is to solve for \( x \).
To do this, divide both sides of the equation by 0.94:
  • \( x = \frac{50,000}{0.94} \)

Performing the division gives:
  • \( x \approx 53,191.49 \)

This final step where we isolate the variable and compute its value is crucial for finding the solution to the equation.

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