Determine The Number That Makes The Following Statement True. 53 − ( A certain number ) = 65 53 - (\text{a Certain Number}) = 65 53 − ( A certain number ) = 65

Mar 9, 2025 by ADMIN 160 views

**Solving for the Missing Number in an Equation**

Introduction

In mathematics, equations are used to represent relationships between variables and constants. Solving for a missing number in an equation involves isolating the variable and finding its value. In this article, we will determine the number that makes the statement $53 - (\text{a certain number}) = 65$ true.

Understanding the Equation

The given equation is $53 - (\text{a certain number}) = 65$ . To solve for the missing number, we need to isolate the variable. The equation can be rewritten as $53 - x = 65$ , where $x$ represents the missing number.

Step 1: Isolate the Variable

To isolate the variable, we need to get rid of the constant term on the same side of the equation. In this case, we can add $x$ to both sides of the equation to get rid of the $-x$ term.

53 - x + x = 65 + x

Simplifying the equation, we get:

53 = 65 + x

Step 2: Solve for the Variable

Now that we have isolated the variable, we can solve for its value. To do this, we need to get rid of the constant term on the same side of the equation. In this case, we can subtract 65 from both sides of the equation to get rid of the 65 term.

53 - 65 = 65 + x - 65

Simplifying the equation, we get:

-12 = x

Conclusion

Therefore, the number that makes the statement $53 - (\text{a certain number}) = 65$ true is $-12$ .

Real-World Applications

Solving for missing numbers in equations has many real-world applications. For example, in finance, solving for missing numbers in equations can help investors determine the value of a stock or bond. In science, solving for missing numbers in equations can help researchers determine the value of a variable in a scientific experiment.

Tips and Tricks

When solving for missing numbers in equations, it's essential to follow the order of operations (PEMDAS):

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following the order of operations, you can ensure that you solve for the missing number correctly.

Common Mistakes

When solving for missing numbers in equations, some common mistakes to avoid include:

Not following the order of operations
Not isolating the variable correctly
Not checking the solution for validity

By avoiding these common mistakes, you can ensure that you solve for the missing number correctly.

Practice Problems

To practice solving for missing numbers in equations, try the following problems:

Solve for the missing number in the equation $2x + 5 = 11$ .
Solve for the missing number in the equation $x - 3 = 7$ .
Solve for the missing number in the equation $4x = 24$ .

By practicing solving for missing numbers in equations, you can become more confident and proficient in solving these types of problems.

Conclusion

Introduction

In our previous article, we discussed how to solve for missing numbers in equations. In this article, we will answer some frequently asked questions about solving for missing numbers in equations.

Q: What is the first step in solving for a missing number in an equation?

A: The first step in solving for a missing number in an equation is to isolate the variable. This involves getting rid of any constant terms on the same side of the equation.

Q: How do I isolate the variable in an equation?

A: To isolate the variable, you can add or subtract the same value to both sides of the equation. For example, if you have the equation $x + 3 = 7$ , you can subtract 3 from both sides to get $x = 4$ .

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that you solve the equation correctly. If you don't follow the order of operations, you may get the wrong answer.

Q: What are some common mistakes to avoid when solving for missing numbers in equations?

A: Some common mistakes to avoid when solving for missing numbers in equations include:

Not following the order of operations
Not isolating the variable correctly
Not checking the solution for validity

Q: How do I check the solution for validity?

A: To check the solution for validity, you can plug the solution back into the original equation and see if it is true. For example, if you have the equation $x + 3 = 7$ and you solve for $x$ to get $x = 4$ , you can plug $x = 4$ back into the original equation to get $4 + 3 = 7$ , which is true.

Q: What are some real-world applications of solving for missing numbers in equations?

A: Solving for missing numbers in equations has many real-world applications, including:

Finance: Solving for missing numbers in equations can help investors determine the value of a stock or bond.
Science: Solving for missing numbers in equations can help researchers determine the value of a variable in a scientific experiment.
Engineering: Solving for missing numbers in equations can help engineers design and build complex systems.

Q: How can I practice solving for missing numbers in equations?

A: You can practice solving for missing numbers in equations by working through practice problems, such as those found in math textbooks or online resources. You can also try solving for missing numbers in equations that are relevant to your own life, such as calculating the cost of a product or determining the value of a variable in a scientific experiment.

Conclusion

In conclusion, solving for missing numbers in equations is a fundamental concept in mathematics. By following the steps outlined in this article and practicing solving for missing numbers in equations, you can become more confident and proficient in solving these types of problems. Remember to follow the order of operations and avoid common mistakes to ensure that you solve for the missing number correctly.