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Chapter 2: Problem 42

Solve equation, and check your solution. \(-3.9 x=32.76\)

Short Answer

Expert verified
x = -8.4, checked and correct.

Step by step solution

01

Isolate the variable

Divide both sides of the equation by -3.9 to isolate the variable x. The equation becomes: \[ x = \frac{32.76}{-3.9}\]
02

Perform the arithmetic

Calculate \(\frac{32.76}{-3.9}\) to find x. \[ x = -8.4\]
03

Check the solution

Substitute x = -8.4 back into the original equation to verify if it holds true.\[-3.9 \times (-8.4) = 32.76\]Simplify the left side:\[32.76 = 32.76\]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.

Isolating the Variable
When solving a linear equation like \(-3.9x = 32.76\), the first step is to isolate the variable (in this case, x). Isolating the variable means getting x by itself on one side of the equation. To do this, we need to reverse the operation currently being performed on x.

Since x is being multiplied by -3.9, we divide both sides of the equation by -3.9. Remember, whatever you do to one side of the equation, you must do to the other.

So, we have:
\[ x = \frac{32.76}{-3.9} \]
This step ensures that x is now isolated on the left-hand side.
Performing Arithmetic Operations
Once we have isolated the variable, we perform the necessary arithmetic operations to find its value. In our equation, we need to calculate:

\[ x = \frac{32.76}{-3.9} \]
When you divide 32.76 by -3.9, you get -8.4. Therefore:

\[ x = -8.4 \]
It鈥檚 crucial to follow proper arithmetic rules while performing these calculations to ensure accuracy. Use a calculator if needed to verify your division.
Checking Solutions
After finding the value of x, it is very important to check if this solution is correct. We do this by substituting x back into the original equation. This helps verify that the original equation is true when x is substituted.

Your original equation is:
\(-3.9x = 32.76\)
Now substitute x = -8.4:
\(-3.9 \times (-8.4) = 32.76\)
Simplifying the left side, we get:
\[ 32.76 = 32.76 \]
Since both sides of the equation are equal, the solution x = -8.4 is correct.

Always remember this checking step, as it ensures that you haven鈥檛 made any mistakes in your calculations.

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