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Chapter 2: Problem 48

Solve each equation, and check the solution. $$ -3.9 x=32.76 $$

Short Answer

Expert verified
x = -8.4

Step by step solution

01

- Isolate the Variable

To solve for the variable x, divide both sides of the equation by -3.9. This will isolate x on one side of the equation. So, \[ x = \frac{32.76}{-3.9} \]
02

- Perform the Division

Now, divide 32.76 by -3.9 to get the value of x. \[ x = \frac{32.76}{-3.9} = -8.4 \]
03

- Check the Solution

Substitute x = -8.4 back into the original equation to verify the solution: \[ -3.9 (-8.4) = 32.76 \] Calculate the left-hand side: \[ 32.76 = 32.76 \] Since both sides of the equation are equal, our solution x = -8.4 is correct.

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Key Concepts

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

Isolation of Variables
Isolating the variable is the first step in solving linear equations. This involves manipulating the equation to get your variable, in this case, x, alone on one side of the equation.
In the exercise, the equation given is \( -3.9x = 32.76 \).
To isolate x, we need to undo the multiplication that is happening to it by \( -3.9 \). This is done through division since it is the inverse operation of multiplication.
We divide both sides of the equation by -3.9, which isolates x.
Now, the equation looks like this:
\[ x = \frac{32.76}{-3.9} \].
Division in Equations
Division is often used in solving linear equations to isolate variables.
After isolating x by dividing both sides by -3.9, we need to perform the actual division:
\[ x = \frac{32.76}{-3.9} \]
Perform the division:
\[ \frac{32.76}{-3.9} = -8.4 \]
This simplifies the equation to:
\[ x = -8.4 \]
By correctly performing the division, you find the value of the variable x.
Verification of Solutions
Verifying your solution is a crucial step.
Once you've found that x = -8.4, you need to ensure that this is correct.
To verify, substitute x = -8.4 back into the original equation:
\[ -3.9(-8.4) = 32.76 \]
Calculate the left-hand side:
\[ 32.76 = 32.76 \]
Both sides of the equation should be equal, confirming that the solution is correct.
Verification ensures that no mistakes were made in the process and the solution is correct.

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