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Chapter 2: Problem 55

Solve equation, and check your solution. \(-0.3 x=9\)

Short Answer

Expert verified
x = -30

Step by step solution

01

- Isolate the Variable

First, we need to isolate the variable x. To do this, divide both sides of the equation by -0.3: \[-0.3x = 9\]\[x = \frac{9}{-0.3}\]
02

- Simplify the Equation

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

- Check the Solution

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

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Key Concepts

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

headline of the respective core concept
To effectively solve any linear equation, it's crucial to isolate the variable. This means that we want the variable (in this case, x) to be by itself on one side of the equation. Given the equation \(-0.3x = 9\), our goal is to get x on one side and a number on the other. We achieve this by using inverse operations, such as addition, subtraction, multiplication, and division.

In our specific example, we divide both sides of the equation by -0.3 to isolate x. This step transforms the equation to:
\[x = \frac{9}{-0.3}\]
This makes sure that the x is alone on one side of the equation, which is essential for finding its value.
headline of the respective core concept
When isolating the variable involves division by a negative number, it's important to remember two key things:

  • Division of two numbers with different signs results in a negative number.
  • Dividing by decimal numbers follows the same principles as dividing by whole numbers, but care must be taken to manage the decimal point.

Let's look at the example again:

\[x = \frac{9}{-0.3}\]
When we divide, we get:

\[x = -30\]
Here, 9 divided by -0.3 results in -30 because 9 divided by 0.3 is 30, and applying the negative sign gives us -30.

Always double-check your arithmetic, especially when dealing with negative and decimal numbers.
headline of the respective core concept
After solving a linear equation, checking your solution is an essential step to ensure its correctness. This involves substituting the found value of the variable back into the original equation and verifying that both sides are equal.

In our example, we found x to be -30. We substitute this back into the original equation:

\[-0.3(-30) = 9\]
Calculate the left-hand side:

\[0.3 \times 30 = 9\]
As expected, both sides of the equation balance out, confirming that our solution is indeed correct.

Always make it a habit to check your solutions to catch any possible errors and confirm the accuracy of your work.

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