Solve For $k$.$125 \ \textless \ K + 50$

Feb 26, 2025 by ADMIN 47 views

Solving for k in the Inequality 125 < k + 50

Introduction

In mathematics, inequalities are used to compare the values of different expressions. They are an essential part of algebra and are used to solve a wide range of problems. In this article, we will focus on solving for k in the inequality 125 < k + 50. This inequality involves a simple linear expression and can be solved using basic algebraic techniques.

Understanding the Inequality

The given inequality is 125 < k + 50. This means that the value of k + 50 is greater than 125. To solve for k, we need to isolate the variable k on one side of the inequality.

Isolating k

To isolate k, we need to subtract 50 from both sides of the inequality. This will give us the value of k.

Subtracting 50 from Both Sides

When we subtract 50 from both sides of the inequality, we get:

125 < k + 50 125 - 50 < k + 50 - 50 75 < k

Conclusion

In this article, we solved for k in the inequality 125 < k + 50. We used basic algebraic techniques to isolate the variable k and found that k is greater than 75.

Step-by-Step Solution

Here's a step-by-step solution to the problem:

Write down the given inequality: 125 < k + 50
Subtract 50 from both sides of the inequality: 125 - 50 < k + 50 - 50
Simplify the inequality: 75 < k

Example Problems

Here are a few example problems that involve solving for k in inequalities:

150 < k + 20
200 > k - 30
250 < k + 10

Tips and Tricks

Here are a few tips and tricks that can help you solve for k in inequalities:

Always read the inequality carefully and understand what it means.
Use basic algebraic techniques such as addition, subtraction, multiplication, and division to isolate the variable k.
Make sure to check your work by plugging in a value for k and verifying that the inequality holds true.

Real-World Applications

Solving for k in inequalities has many real-world applications. Here are a few examples:

In finance, inequalities can be used to compare the values of different investments.
In science, inequalities can be used to compare the values of different physical quantities.
In engineering, inequalities can be used to compare the values of different design parameters.

Conclusion

In this article, we solved for k in the inequality 125 < k + 50. We used basic algebraic techniques to isolate the variable k and found that k is greater than 75. Solving for k in inequalities has many real-world applications and is an essential part of algebra.

Frequently Asked Questions

Here are a few frequently asked questions about solving for k in inequalities:

Q: What is the value of k in the inequality 125 < k + 50? A: The value of k is greater than 75.
Q: How do I solve for k in an inequality? A: Use basic algebraic techniques such as addition, subtraction, multiplication, and division to isolate the variable k.
Q: What are some real-world applications of solving for k in inequalities? A: Solving for k in inequalities has many real-world applications, including finance, science, and engineering.

Final Thoughts

Solving for k in inequalities is an essential part of algebra and has many real-world applications. By following the steps outlined in this article, you can solve for k in inequalities and apply the techniques to a wide range of problems.

Introduction

In our previous article, we solved for k in the inequality 125 < k + 50. We used basic algebraic techniques to isolate the variable k and found that k is greater than 75. In this article, we will answer some frequently asked questions about solving for k in inequalities.

Q&A

Q: What is the difference between an inequality and an equation?

A: An inequality is a statement that compares two expressions using a relation such as <, >, ≤, or ≥. An equation is a statement that says two expressions are equal. For example, 2x + 3 < 5 is an inequality, while 2x + 3 = 5 is an equation.

Q: How do I solve for k in an inequality?

A: To solve for k in an inequality, you need to isolate the variable k on one side of the inequality. You can do this by adding or subtracting the same value from both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero value.

Q: What are some common mistakes to avoid when solving for k in inequalities?

A: Some common mistakes to avoid when solving for k in inequalities include:

Not reading the inequality carefully and understanding what it means
Not isolating the variable k on one side of the inequality
Not checking your work by plugging in a value for k and verifying that the inequality holds true
Not considering the direction of the inequality (e.g. < vs. >)

Q: How do I know which direction to solve the inequality in?

A: To determine which direction to solve the inequality in, you need to consider the direction of the inequality. If the inequality is <, you need to solve for k in the direction of increasing values. If the inequality is >, you need to solve for k in the direction of decreasing values.

Q: Can I use the same steps to solve for k in an inequality as I would to solve for x in an equation?

A: While the steps to solve for k in an inequality are similar to the steps to solve for x in an equation, there are some key differences. When solving for k in an inequality, you need to consider the direction of the inequality and make sure to isolate the variable k on one side of the inequality.

Q: How do I check my work when solving for k in an inequality?

A: To check your work when solving for k in an inequality, you need to plug in a value for k and verify that the inequality holds true. You can also use a number line or a graph to visualize the solution to the inequality.

Q: Can I use a calculator to solve for k in an inequality?

A: While a calculator can be a useful tool for solving for k in an inequality, it is not always necessary. In many cases, you can solve for k in an inequality using basic algebraic techniques and a pencil and paper.

Conclusion

Solving for k in inequalities is an essential part of algebra and has many real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can solve for k in inequalities and apply the techniques to a wide range of problems.

Frequently Asked Questions

Here are a few frequently asked questions about solving for k in inequalities:

Q: What is the value of k in the inequality 125 < k + 50? A: The value of k is greater than 75.
Q: How do I solve for k in an inequality? A: Use basic algebraic techniques such as addition, subtraction, multiplication, and division to isolate the variable k.
Q: What are some real-world applications of solving for k in inequalities? A: Solving for k in inequalities has many real-world applications, including finance, science, and engineering.