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Chapter 9: Problem 63

Solve the equation \(x-0.09 x=72,800\)

Short Answer

Expert verified
x = 80,000

Step by step solution

01

- Combine like terms

Combine the terms involving x on the left side of the equation. The equation is given as: \( x - 0.09x = 72,800 \). Find the common factor (x) and simplify, which results in: \( (1 - 0.09)x = 72,800 \) or \( 0.91x = 72,800 \)
02

- Solve for x

To isolate \(x\), divide both sides of the equation by 0.91. This gives: \( x = \frac{72,800}{0.91} \). Now, perform the division: \( x = 80,000 \)

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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 means simplifying expressions by adding or subtracting the coefficients of similar variables. In the equation given, we have two terms that involve x: \(x\) and \(0.09x\). These are 'like terms' because they both have the variable x. To combine them, we factor out the common variable (x). This means we take:
\( x - 0.09x \) and write it as: \((1 - 0.09)x\).
Simplify \((1 - 0.09)\) to get \(0.91x\). Now, the equation is easier to work with: \(0.91x = 72,800\).
Isolation of Variable
Isolation of the variable involves getting the variable, in this case, x, by itself on one side of the equation. After combining like terms, we have: \(0.91x = 72,800\). To isolate x, we need to get rid of the coefficient 0.91. We do this by performing the opposite operation. Since 0.91 is multiplied by x, we divide both sides of the equation by 0.91.
This step looks like: \(x = \frac{72,800}{0.91}\). Dividing the right-hand side by 0.91 isolates x.
Division in Equations
Division in equations applies when we need to isolate a variable by removing a coefficient. In our equation, \(0.91x = 72,800\), x is multiplied by 0.91. To solve for x, we divide both sides by 0.91:
\(x = \frac{72,800}{0.91}\). This operation simplifies to: \(x = 80,000\).
It's important to execute the division correctly to find the accurate value of x.
This technique is common in solving linear equations and helps simplify equations to find the solution quickly.

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