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Chapter 4: Problem 37

Solve the equations and inequalities. $$0.3 x-0.25 x=2$$

Short Answer

Expert verified
x = 40

Step by step solution

01

Combine like terms

Combine the terms on the left-hand side of the equation: \(0.3x - 0.25x\).
02

Simplify the equation

Simplify the combined like terms: \(0.3x - 0.25x = 0.05x\). The equation now looks like: \(0.05x = 2\).
03

Solve for x

Divide both sides of the equation by 0.05 to isolate \(x\): \(x = \frac{2}{0.05}\).
04

Calculate the result

Perform the division to find the value of \(x\): \(x = 40\).

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Key Concepts

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

Combining Like Terms
When solving linear equations, one of the first steps often involves combining like terms. Like terms are terms that have the same variable raised to the same power. In our given exercise, the like terms are \(0.3x\) and \(0.25x\). Combining like terms means adding or subtracting these terms to simplify the equation. For our exercise, we subtracted \(0.25x\) from \(0.3x\), which gave us \(0.05x\). This step makes the equation easier to solve. Look for coefficients (the numbers in front of the variables) and combine them to reduce complexity.
Isolating the Variable
Isolating the variable means getting the variable (in this case, \(x\)) on one side of the equation by itself. This is crucial for solving the equation. Once we simplified \(0.3x - 0.25x\) to \(0.05x\), our equation turned into \(0.05x = 2\). To isolate \(x\), we need to get rid of the \(0.05\) coefficient. We do this by dividing both sides of the equation by \(0.05\). This results in \(x = \frac{2}{0.05}\), effectively isolating \(x\) and making it easy to solve.
Simplifying Expressions
Simplifying expressions is a fundamental step in solving equations. In our example, simplifying \(0.3x - 0.25x\) to \(0.05x\) involved basic arithmetic. Simplification helps to make complex expressions more manageable. After isolating the variable, the last simplification step involved calculating \(x = \frac{2}{0.05}\). Performing this division gave us \(x = 40\). By breaking down and simplifying each part of the equation, we make it easier to understand and solve. Always aim to simplify expressions at each step to keep the problem straightforward.

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