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Chapter 1: Problem 89

$$\text { Solve } x-0.001 x=9990$$.

Short Answer

Expert verified
x = 10000

Step by step solution

01

Combine like terms

The equation is initially given as \(x - 0.001x = 9990\). Combine the like terms on the left-hand side by factoring out \(x\).
02

Factor out x

Rewrite the equation as:\[x(1 - 0.001) = 9990\]Simplify the factor inside the parenthesis.
03

Simplify the parenthesis

Calculate inside the parentheses: \[1 - 0.001 = 0.999\].So, the equation becomes \[0.999x = 9990\].
04

Solve for x

To isolate \(x\), divide both sides of the equation by \(0.999\):\[x = \frac{9990}{0.999}\].
05

Calculate the quotient

Perform the division:\[x = 10000\].

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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 crucial when solving linear equations. In the exercise, the equation starts with: \(x - 0.001x = 9990\).
You need to combine similar terms, which are the terms that have the same variable.
In this case, both terms on the left side have the variable \(x\). To combine them, factor out the common variable: \(x(1 - 0.001) = 9990\). This step reduces the complexity and gets you closer to the solution.
Factoring
Factoring helps simplify expressions by grouping terms efficiently. In the equation \(x - 0.001x = 9990\), we factored out \(x\) to get \(x(1 - 0.001) = 9990\).
This makes it easier to further simplify the expression. Think of factoring as a way of 're-grouping' terms to make the equation less complex.
In this exercise, factoring allows us to handle the inside of the parenthesis separately, making the overall solution simpler.
Simplifying Expressions
Simplifying expressions is about reducing an equation to its simplest form. After factoring out \(x\) and rewriting as \(x(1 - 0.001) = 9990\), focus on simplifying inside the parenthesis.
Calculate \(1 - 0.001\): \(0.999\).
Thus, \(x(0.999) = 9990\).
Remember, always break down complex expressions into simpler parts. This makes it easier to isolate variables and solve the equation.
Isolating Variables
Isolating the variable is the final step in solving equations. You must get the variable on one side by itself.
In the equation \(0.999x = 9990\), isolate \(x\) by dividing both sides by \(0.999\): \(x = \frac{9990}{0.999}\).
This gives you \(x = 10000\).
Always perform the same operation on both sides of the equation to keep it balanced while isolating the variable.

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