Use The Inequality Created By The Statement $p$ Less 13 Is Fewer Than 24 To Solve For $p$.A. $p \ \textless \ 11$B. $p \leq 11$C. $p \ \textless \ 37$D. $p \leq 37$
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Introduction
In mathematics, inequalities are used to compare two or more values. 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 inequalities, specifically the inequality created by the statement "$p$ less 13 is fewer than 24". We will use this inequality to solve for $p$ and explore the different options available.
Understanding the Inequality
The given inequality is "$p$ less 13 is fewer than 24". This can be written mathematically as:
To solve for $p$, we need to isolate the variable $p$ on one side of the inequality.
Solving the Inequality
To solve the inequality, we need to add 13 to both sides of the inequality. This will give us:
Simplifying the inequality, we get:
Analyzing the Options
Now that we have solved the inequality, let's analyze the options available:
- A. $p \ \textless \ 11$: This option is incorrect because the inequality we solved is $p < 37$, not $p < 11$.
- B. $p \leq 11$: This option is also incorrect because the inequality we solved is $p < 37$, not $p \leq 11$.
- C. $p \ \textless \ 37$: This option is correct because the inequality we solved is $p < 37$.
- D. $p \leq 37$: This option is incorrect because the inequality we solved is $p < 37$, not $p \leq 37$.
Conclusion
In conclusion, the correct answer is C. $p \ \textless \ 37$. This is because the inequality we solved is $p < 37$, and option C correctly represents this inequality.
Frequently Asked Questions
Q: What is an inequality?
A: An inequality is a mathematical statement that compares two or more values. It is used to solve a wide range of problems in algebra.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable on one side of the inequality. This can be done by adding or subtracting the same value from both sides of the inequality.
Q: What is the difference between an inequality and an equation?
A: An equation is a mathematical statement that states that two or more values are equal. An inequality, on the other hand, states that two or more values are not equal.
Examples
Example 1
Solve the inequality $x + 5 < 10$.
To solve this inequality, we need to subtract 5 from both sides of the inequality. This gives us:
Simplifying the inequality, we get:
Example 2
Solve the inequality $y - 3 > 2$.
To solve this inequality, we need to add 3 to both sides of the inequality. This gives us:
Simplifying the inequality, we get:
Tips and Tricks
Tip 1
When solving an inequality, make sure to isolate the variable on one side of the inequality.
Tip 2
When adding or subtracting the same value from both sides of an inequality, make sure to do it to both sides of the inequality.
Tip 3
When multiplying or dividing both sides of an inequality by a negative number, make sure to flip the direction of the inequality.
Conclusion
In conclusion, solving inequalities is an essential part of algebra. By following the steps outlined in this article, you can solve inequalities with ease. Remember to isolate the variable on one side of the inequality and to add or subtract the same value from both sides of the inequality. With practice, you will become proficient in solving inequalities and be able to tackle a wide range of problems in algebra.
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Introduction
In our previous article, we discussed how to solve inequalities, specifically the inequality created by the statement "$p$ less 13 is fewer than 24". We also explored the different options available and analyzed the correct answer. In this article, we will continue to provide a Q&A guide on solving inequalities.
Q&A
Q: What is an inequality?
A: An inequality is a mathematical statement that compares two or more values. It is used to solve a wide range of problems in algebra.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable on one side of the inequality. This can be done by adding or subtracting the same value from both sides of the inequality.
Q: What is the difference between an inequality and an equation?
A: An equation is a mathematical statement that states that two or more values are equal. An inequality, on the other hand, states that two or more values are not equal.
Q: Can I use the same steps to solve all types of inequalities?
A: No, the steps to solve an inequality may vary depending on the type of inequality. For example, when solving a linear inequality, you can add or subtract the same value from both sides of the inequality. However, when solving a quadratic inequality, you may need to use more complex methods such as factoring or using the quadratic formula.
Q: How do I know which method to use when solving an inequality?
A: The method you use to solve an inequality will depend on the type of inequality and the values involved. For example, if you are solving a linear inequality with a single variable, you can use the method of adding or subtracting the same value from both sides of the inequality. However, if you are solving a quadratic inequality with multiple variables, you may need to use more complex methods such as factoring or using the quadratic formula.
Q: Can I use a calculator to solve an inequality?
A: Yes, you can use a calculator to solve an inequality. However, it is always a good idea to check your work by hand to make sure that the solution is correct.
Q: How do I graph an inequality on a number line?
A: To graph an inequality on a number line, you need to plot the values that satisfy the inequality. For example, if you are graphing the inequality $x > 2$, you would plot the values 3, 4, 5, and so on.
Q: Can I use the same graph to represent multiple inequalities?
A: No, each inequality should have its own graph. However, you can use the same graph to represent multiple inequalities if they have the same solution set.
Examples
Example 1
Solve the inequality $x + 5 < 10$.
To solve this inequality, we need to subtract 5 from both sides of the inequality. This gives us:
Simplifying the inequality, we get:
Example 2
Solve the inequality $y - 3 > 2$.
To solve this inequality, we need to add 3 to both sides of the inequality. This gives us:
Simplifying the inequality, we get:
Tips and Tricks
Tip 1
When solving an inequality, make sure to isolate the variable on one side of the inequality.
Tip 2
When adding or subtracting the same value from both sides of an inequality, make sure to do it to both sides of the inequality.
Tip 3
When multiplying or dividing both sides of an inequality by a negative number, make sure to flip the direction of the inequality.
Tip 4
When graphing an inequality on a number line, make sure to plot the values that satisfy the inequality.
Conclusion
In conclusion, solving inequalities is an essential part of algebra. By following the steps outlined in this article, you can solve inequalities with ease. Remember to isolate the variable on one side of the inequality and to add or subtract the same value from both sides of the inequality. With practice, you will become proficient in solving inequalities and be able to tackle a wide range of problems in algebra.
Frequently Asked Questions
Q: What is the difference between a linear inequality and a quadratic inequality?
A: A linear inequality is an inequality that can be written in the form $ax + b < c$, where $a$, $b$, and $c$ are constants. A quadratic inequality, on the other hand, is an inequality that can be written in the form $ax^2 + bx + c < 0$, where $a$, $b$, and $c$ are constants.
Q: How do I solve a quadratic inequality?
A: To solve a quadratic inequality, you can use methods such as factoring or using the quadratic formula. You can also use a graphing calculator to graph the quadratic function and determine the solution set.
Q: Can I use a calculator to solve a quadratic inequality?
A: Yes, you can use a calculator to solve a quadratic inequality. However, it is always a good idea to check your work by hand to make sure that the solution is correct.
Q: How do I graph a quadratic inequality on a number line?
A: To graph a quadratic inequality on a number line, you need to plot the values that satisfy the inequality. For example, if you are graphing the inequality $x^2 + 4x + 4 < 0$, you would plot the values that make the quadratic function negative.
Q: Can I use the same graph to represent multiple quadratic inequalities?
A: No, each quadratic inequality should have its own graph. However, you can use the same graph to represent multiple quadratic inequalities if they have the same solution set.