Problem 326 In the following exercises, solv... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 326

In the following exercises, solve each equation. $$ n-18=31 $$

Short Answer

Expert verified

The solution is n = 49.

Step by step solution

- Identify the Variable

The equation given is -18 = 31. Identify the variable which is 'n'.

- Isolate the Variable

To isolate 'n', add 18 to both sides of the equation. This action will cancel out the -18 on the left side.$ n - 18 + 18 = 31 + 18 $

- Simplify Both Sides

Simplify the equation by performing the addition on both sides:$ n = 49 $

- Verify the Solution

Substitute the value of 'n' back into the original equation to ensure it is correct:$ 49 - 18 = 31 $, which holds true.

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Key Concepts

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

Solving Linear Equations

Linear equations are straightforward mathematical expressions where the highest exponent of the variable is one. In our example, the equation is: $ n - 18 = 31 $. Here, 'n' is the variable we need to solve for. Solving linear equations generally involves isolating the variable on one side of the equation. Once isolated, we can determine its value easily.

Understanding the structure of linear equations is crucial. They typically look like this: $ ax + b = c $, where 'a', 'b', and 'c' are constants.
The goal is to solve for 'x'.

Isolating Variables

To solve $ n - 18 = 31 $, we need to isolate the variable 'n'. Isolating a variable means getting it alone on one side of the equation.

Here's how:

Identify the variable you need to solve for, which is 'n' in our case.
Perform the same operation on both sides of the equation to maintain balance.

For $ n - 18 = 31 $:
Add 18 to both sides:
$ n - 18 + 18 = 31 + 18 $
Simplify both sides:
$ n = 49 $

Now, 'n' is isolated, and we can see its value clearly.

Verifying Solutions

Once we've solved for the variable, it's essential to verify our solution. Verification ensures that the solution is correct and that no mistakes were made during the process.

To verify our solution for $ n - 18 = 31 $:

Substitute the value of 'n' back into the original equation.
Check if both sides of the equation are equal.

Plugging in $ n = 49 $:
$ 49 - 18 = 31 $
Simplify:
$ 31 = 31 $

Since both sides are equal, our solution $ n = 49 $ is correct.
This step checks our work and confirms that the solution satisfies the original equation.

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91影视

In the following exercises, solve each equation. $$ n-18=31 $$

Short Answer

Step by step solution

- Identify the Variable

- Isolate the Variable

- Simplify Both Sides

- Verify the Solution

Key Concepts

Solving Linear Equations

Isolating Variables

Verifying Solutions

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