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Chapter 2: Problem 41

Solve each equation, and check the solution. $$ -0.3 x=9 $$

Short Answer

Expert verified
x = -30

Step by step solution

01

- Isolate the variable

To solve for \( x \), divide both sides of the equation by \(-0.3\). This will cancel out the coefficient of \( x \) on the left side of the equation:\[ x = \frac{9}{-0.3} \]
02

- Simplify the equation

Simplify the right side of the equation:\[ x = \frac{9}{-0.3} = -30 \]
03

- Check the solution

Substitute \( x = -30 \) back into the original equation to verify the solution:\[-0.3(-30) = 9\]Solve the left side:\[ 9 = 9 \]Since both sides are equal, the solution is verified.

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Key Concepts

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

solve equations
Solving an equation is like finding the value of the variable that makes the equation true. In our example, we need to find the value of \(x\) in the equation \( -0.3 x = 9 \). Think of an equation as a balance scale. The goal is to keep the equation balanced while finding the value of \(x\). Always perform the same operation on both sides of the equation. This keeps the equation balanced.
Steps to solve equations:
  • Identify the operations performed on the variable.
In this case, multiplication by \(-0.3\).
  • Apply the inverse operations to isolate the variable.
  • Verify the solution to make sure it works in the original equation.
isolate variable
Isolating the variable means getting the variable alone on one side of the equation. In our example, the variable is \(x\). It's currently multiplied by \(-0.3\) in the equation \( -0.3 x = 9 \). To isolate \(x\), we need to get rid of the \(-0.3\). We do this by dividing both sides of the equation by \(-0.3\). This inverse operation cancels out the \(-0.3\) next to the \(x\):

\[ x = \frac{9}{-0.3} \]

Simplifying the division, we get:

\[ x = -30 \]

Now, \(x\) is isolated, meaning we have found the value that satisfies the equation.
check solution
Checking the solution is crucial to ensure the answer is correct. After isolating the variable and solving for \(x\) in the equation \( -0.3 x = 9 \), we found that \( x = -30 \). To check our solution, we substitute \(x\) back into the original equation:

\[ -0.3(-30) = 9 \]

Simplifying the left side of the equation:

\[ 9 = 9 \].

Since both sides of the equation are equal, our solution \( x = -30 \) is correct. Always check your solution to verify accuracy.

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