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.
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