Problem 42 Solve using the multiplication p... [FREE SOLUTION]

Chapter 2: Problem 42

Solve using the multiplication principle. Don't forget to check! $$ 3 x=39 $$

Short Answer

Expert verified

x = 13

Step by step solution

- Isolate the Variable

The equation to solve is $3x = 39$. To isolate the variable, divide both sides of the equation by 3. $\frac{3x}{3} = \frac{39}{3}$

- Simplify the Equation

Simplify both sides of the equation: $x = 13$

- Check the Solution

To verify the solution, substitute $x = 13$ back into the original equation: $3(13) = 39$. Since both sides 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.

solving equations

Solving equations is a foundational skill in mathematics. The goal is to find the value of an unknown variable that makes the equation true. An equation states that two expressions are equal. In solving equations, we perform operations to both sides of the equation to keep this balance. Always remember, if you do something to one side, you must do it to the other side as well.
To solve equations, follow these general steps:

Identify the variable and the constants.
Apply inverse operations to isolate the variable.
Simplify both sides of the equation as needed.
Check your solution by substituting it back into the original equation.

Let's explore how these steps apply specifically to the multiplication principle.

isolate the variable

The key step in solving an equation is to isolate the variable, meaning to get the variable alone on one side of the equation. In the given exercise, we need to solve for x in the equation $3x = 39$. Here鈥檚 how this process works for our example:

We have the equation $3x = 39$.
The coefficient of x here is 3, which means 3 is multiplied by x. To isolate x, we must do the opposite operation, which is division.
So, we divide both sides of the equation by 3: \frac{3x}{3} = \frac{39}{3}\.
This simplifies to: \x = 13\.

We have successfully isolated the variable. Now, x is alone on one side of the equation, and we have determined that x equals 13.

verify the solution

After isolating the variable and finding the solution, it is crucial to verify that your solution is correct. This step ensures that no mistakes were made during calculation. Here鈥檚 how to verify the solution for our example:

We found that x = 13.
To check, substitute x back into the original equation $3x = 39$.
Replace x with 13: \3(13) = 39\.
Perform the multiplication: 3 times 13 equals 39.
Since the left side (39) equals the right side (39), our solution is correct.

Verification confirms that our original solution x = 13 holds true for the given equation. Always take this step to ensure accuracy in solving equations.

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91影视

Solve using the multiplication principle. Don't forget to check! $$ 3 x=39 $$

Short Answer

Step by step solution

- Isolate the Variable

- Simplify the Equation

- Check the Solution

Key Concepts

solving equations

isolate the variable

verify the solution

One App. One Place for Learning.

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