/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 94 Solve each equation. $$ 0.4 ... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 94

Solve each equation. $$ 0.4 x=80 $$

Short Answer

Expert verified
The solution is \( x = 200 \).

Step by step solution

01

- Understand the equation

The given equation is a simple linear equation: \(0.4x = 80\).It implies that 0.4 times some number equals 80.
02

- Isolate the variable (x)

To solve for \(x\), divide both sides of the equation by 0.4:\[\frac{0.4x}{0.4} = \frac{80}{0.4}.\]
03

- Perform the division

Divide 80 by 0.4:\[x = 80 \div 0.4.\]Performing the division gives us:\[x = 200.\]

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Key Concepts

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

linear equations
In algebra, linear equations are equations of the first degree. This means they involve only linear terms, meaning variables are not raised to any power other than one. The general form of a linear equation in one variable can be written as:\[ ax + b = c \]Where \(a\), \(b\), and \(c\) are constants, and \(x\) is the variable. The goal when solving a linear equation is to find the value of the variable that makes the equation true.In the given exercise, the linear equation is:\[ 0.4x = 80 \]Here, \(0.4\) is the coefficient of \(x\), and \(80\) is the constant term on the other side of the equation.
isolating variables
Isolating the variable in an equation means getting the variable by itself on one side of the equation. This usually involves performing inverse operations to both sides of the equation.Starting with step 2 in the given solution, we have the equation:\[ 0.4x = 80 \]To isolate the variable \(x\), we need to remove the coefficient 0.4 that is multiplied by it. We do this by dividing both sides of the equation by 0.4:\[ \frac{0.4x}{0.4} = \frac{80}{0.4} \]This step cancels out the coefficient on the left-hand side, leaving us with \(x\) alone:\[ x = \frac{80}{0.4} \]
division in algebra
Division is one of the basic arithmetic operations we use to solve for variables in algebra. When we need to isolate a variable that is being multiplied by a coefficient, division allows us to cancel out the coefficient.In the exercise, after isolating the variable, we reach the step:\[ x = \frac{80}{0.4} \]To solve this, we actually perform the division:\[ 80 \text{ divided by } 0.4 = 200 \]Hence, the value of \(x\) is 200. Breaking numbers down like this makes it easier to understand why we perform each step and what it achieves in terms of solving the equation.

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