An inequality is an expression that contains a greater than, less than, or equal to sign. Inequalities can have one or more variables and can be solved using algebraic techniques. In this article, we will be looking at how to solve the inequality 5f + 7 > 22. We will go through the steps of solving this inequality and explain the logic behind each step.

## Understanding the Inequality

The inequality 5f + 7 > 22 can be written in a more readable form as 5f > 15. This means that we are looking for the value of f such that when we multiply it by 5 and add 7, the result is greater than 22. To solve this inequality, we need to subtract 7 from both sides and then divide both sides by 5.

## Solving the Inequality

The first step is to subtract 7 from both sides of the inequality. This will give us 5f > 8. Then, we need to divide both sides by 5. This will give us f > 1.6. We can also write this as f > 1.6 or f ≥ 1.6. This means that for the inequality 5f + 7 > 22 to be true, the value of f must be greater than or equal to 1.6.

## Interpreting the Answer

The answer we obtained, f > 1.6 or f ≥ 1.6, can be interpreted as follows: any value of f that is greater than 1.6 will make the inequality true. This means that if we plug in any value of f that is greater than 1.6 into the inequality 5f + 7 > 22, the result will be true.

## Check the Answer

We can check our answer by plugging in a few values of f. For example, if we plug in f = 2, then 5f + 7 = 17. This is greater than 22 and so our answer is correct. Similarly, if we plug in f = 1.5, then 5f + 7 = 8.5 which is less than 22 and so our answer is still correct.

In conclusion, we have looked at how to solve the inequality 5f + 7 > 22. We have gone through the steps of solving this inequality, explained the logic behind each step, and checked our answer by plugging in a few values of f. We have found that the solution is f > 1.6 or f ≥ 1.6. Any value of f that is greater than 1.6 will make the inequality true.

### Related Posts:

- Solving Inequalities in Lesson 14 Solving inequalities is a critical algebraic skill that is necessary for success in secondary math classes. In lesson 14, students will learn how to solve linear and…
- Solving Radical Equations and Inequalities Radical equations and inequalities are an important part of algebra. They involve equations and inequalities which contain square roots and cubes roots. The equations and inequalities require…
- Which Algebraic Expression Represents a Word Description? What is an Algebraic Expression?An algebraic expression is an equation that is used to represent a number or a set of numbers. It includes variables, constants, and…
- 8 Steps to Solve Rational Equations & Inequalities Rational equations and inequalities are algebraic equations or inequalities in which the variables and/or coefficients are rational numbers. Solving these equations involves using the same techniques as…
- Solve This Inequality 3b-7 32 Solving an inequality is a process of finding the values of a variable that makes the inequality true. This means that the solution is the set of…
- In the Expression Above A is a Constant An expression is a combination of variables, numbers and operations which together form a mathematical statement. In an expression, a constant is a value that does not…
- 8 6 Skills Practice Solving Rational Equations and… Solving rational equations and inequalities involves the use of several mathematical skills. These include algebraic equations, rational expressions, and linear equations. Knowing how to correctly solve these…
- What Inequality Describes the Solutions of 2y + 8? Inequality is a mathematical concept that is used to compare two quantities. It is a statement of the form “A is greater than, equal to, or less…
- Which Algebraic Expression Represents Nicholas Tripling His… Algebra is a branch of mathematics with a long history. It's used to solve equations and to answer questions with numerical values. Algebra also helps us to…
- Unit 2 Logic and Proof Homework 1: What to Expect Unit 2 Logic and Proof Homework 1 is an important part of understanding and mastering the principles of logic and proof. This homework assignment is designed to…
- Which Inequality is Equivalent to x 4 9? Inequalities are mathematical statements that compare two values. An inequality can be written using one of the following symbols: , =. In this article, we will discuss…
- Write Algebraic Expressions for Verbal Expressions Writing algebraic expressions for verbal expressions is a crucial skill for any student studying algebra. It is a fundamental part of understanding algebra as it allows you…
- Write and Evaluate the Expression: Comprehension and… An expression is a combination of numbers, symbols, and variables that represent a quantity or value. Expressions can be written in a variety of ways, but all…
- 5 3 Skills Practice Inequalities in One Triangle Inequalities in one triangle are a great way to practice and develop your 5/3 skills. They provide a visual representation of the relationship between the sides of…
- 5 Steps to Solving Multi-Step Inequalities Multi-step inequalities can be daunting, especially for those who are new to solving them. However, once you understand the basic principles and steps, it can make the…
- 6 3 Practice Square Root Functions and Inequalities What are Square Root Functions and Inequalities?Square root functions and inequalities are mathematical equations used to solve problems involving square root functions and their corresponding inequalities. They…
- Understanding Triangle Inequalities in Unit 5 Relationships… Unit 5 Relationships in Triangles Homework 8 focuses on triangle inequalities. Students must understand the rules and principles of triangle inequalities before they can solve any related…