Problem 59 8 more than a certain number is ... [FREE SOLUTION]

91影视

Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 1: Problem 59

8 more than a certain number is 18 . Find the number.

Short Answer

Expert verified

The number is 10.

Step by step solution

Understand the Problem

The problem states that 8 more than a certain number equals 18. This means if you add 8 to an unknown number, you get 18.

Set Up an Equation

Let the unknown number be represented by the variable $ x $. According to the problem, 8 more than this number is 18. This can be translated into the equation: $ x + 8 = 18 $.

Solve for the Unknown Number

To find $ x $, we need to isolate it on one side of the equation. Subtract 8 from both sides of the equation: $ x + 8 - 8 = 18 - 8 $ which simplifies to $ x = 10 $.

Verify the Solution

To ensure the solution is correct, check that 8 more than 10 equals 18. Calculate $ 10 + 8 = 18 $, which is correct. Therefore, the number is indeed 10.

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Key Concepts

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

Understanding the Unknown Variable

In many math problems, we encounter the concept of an "unknown variable." This is simply a number we do not know yet but are trying to find. In algebra, we use variables like $ x, y, $ or $ z $ to stand in for these unknown numbers.
In the exercise, the phrase "a certain number" refers to this unknown number, so we let $ x $ be this variable. This helps us to systematically solve the problem since working with variables allows us to write equations that we can manipulate to find solutions.

Setting Up the Equation

Once we identify the unknown variable, we need to translate the words of the problem into a mathematical equation. Text problems often contain keywords that signal mathematical operations.
In this problem, the phrase "8 more than" tells us to use addition, and "equals 18" signals that the result is 18.
Using the variable $ x $ to represent the unknown number, the problem becomes a mathematical statement:

The unknown number, plus 8, is equal to 18.
This is expressed as $ x + 8 = 18 $.

Setting up an equation accurately is crucial as it forms the foundation for arriving at the correct answer.

Verifying the Solution

After solving an equation, it鈥檚 important to verify that the solution is correct. This step helps ensure that no mistakes were made in earlier steps.
Verification involves substituting the solution back into the original equation to see if it holds true.
In this example, we solved for $ x $ and found that $ x = 10 $. To verify:

Replace $ x $ in the equation $ x + 8 = 18 $ with 10.
Check: $ 10 + 8 = 18 $.

Since both sides of the equation are equal, the solution is correct. This gives us confidence that the unknown number is indeed 10.

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91影视

8 more than a certain number is 18 . Find the number.

Short Answer

Step by step solution

Understand the Problem

Set Up an Equation

Solve for the Unknown Number

Verify the Solution

Key Concepts

Understanding the Unknown Variable

Setting Up the Equation

Verifying the Solution

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