Determine Which Statement Matches Each Inequality.- □ \square □ X \textgreater 10 X \ \textgreater \ 10 X \textgreater 10 - □ \square □ X \textless 10 X \ \textless \ 10 X \textless 10 - □ \square □ X ≥ 10 X \geq 10 X ≥ 10 - □ \square □ X ≤ 10 X \leq 10 X ≤ 10 A. Palesa

In mathematics, inequalities are used to compare the values of two or more expressions. They are an essential part of algebra and are used to solve equations and inequalities. In this article, we will determine which statement matches each inequality.

Understanding Inequalities

Inequalities are mathematical statements that compare two or more expressions using the following symbols:

• Greater than (>): $x > 10$
• Less than (<): $x < 10$
• Greater than or equal to (≥): $x \geq 10$
• Less than or equal to (≤): $x \leq 10$

Analyzing the Inequalities

Let's analyze each inequality and determine which statement matches it.

Inequality 1: $x \ \textgreater \ 10$

This inequality states that $x$ is greater than 10. To determine which statement matches this inequality, we need to find a statement that is true when $x$ is greater than 10.

• Palesa is a statement that is true when $x$ is greater than 10. Therefore, the statement that matches this inequality is: Palesa

Inequality 2: $x \ \textless \ 10$

This inequality states that $x$ is less than 10. To determine which statement matches this inequality, we need to find a statement that is true when $x$ is less than 10.

• Palesa is a statement that is not true when $x$ is less than 10. Therefore, the statement that matches this inequality is: Not Palesa

Inequality 3: $x \geq 10$

This inequality states that $x$ is greater than or equal to 10. To determine which statement matches this inequality, we need to find a statement that is true when $x$ is greater than or equal to 10.

• Palesa is a statement that is true when $x$ is greater than or equal to 10. Therefore, the statement that matches this inequality is: Palesa

Inequality 4: $x \leq 10$

This inequality states that $x$ is less than or equal to 10. To determine which statement matches this inequality, we need to find a statement that is true when $x$ is less than or equal to 10.

• Palesa is a statement that is not true when $x$ is less than or equal to 10. Therefore, the statement that matches this inequality is: Not Palesa

Conclusion

In conclusion, the statements that match each inequality are:

• $x \ \textgreater \ 10$: Palesa
• $x \ \textless \ 10$: Not Palesa
• $x \geq 10$: Palesa
• $x \leq 10$: Not Palesa

Final Answer

The final answer is:

In the previous article, we determined which statement matches each inequality. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information.

Q: What is the difference between $x > 10$ and $x \geq 10$?

A: The difference between $x > 10$ and $x \geq 10$ is that $x > 10$ means that $x$ is strictly greater than 10, while $x \geq 10$ means that $x$ is greater than or equal to 10.

Q: How do I determine which statement matches an inequality?

A: To determine which statement matches an inequality, you need to analyze the inequality and find a statement that is true when the inequality is satisfied. For example, if the inequality is $x > 10$, you need to find a statement that is true when $x$ is greater than 10.

Q: What is the relationship between inequalities and equations?

A: Inequalities and equations are related in that they both involve comparing expressions. However, inequalities involve comparing expressions using the symbols $>$, $<$, $\geq$, and $\leq$, while equations involve comparing expressions using the symbol $=$.

Q: Can I use inequalities to solve equations?

A: Yes, you can use inequalities to solve equations. For example, if you have the equation $x + 2 = 10$, you can use an inequality to find the solution. In this case, you can use the inequality $x + 2 > 10$ to find the solution.

Q: How do I graph inequalities on a number line?

A: To graph an inequality on a number line, you need to plot a point on the number line that satisfies the inequality and then shade the region to the left or right of the point, depending on the direction of the inequality.

Q: Can I use inequalities to compare fractions?

A: Yes, you can use inequalities to compare fractions. For example, if you have the fractions $\frac{1}{2}$ and $\frac{3}{4}$, you can use an inequality to compare them. In this case, you can use the inequality $\frac{1}{2} < \frac{3}{4}$ to compare the fractions.

Q: How do I solve systems of inequalities?

A: To solve a system of inequalities, you need to find the solution that satisfies all the inequalities in the system. You can use various methods, such as graphing or substitution, to solve a system of inequalities.

Q: Can I use inequalities to solve word problems?

A: Yes, you can use inequalities to solve word problems. For example, if you have a word problem that involves comparing quantities, you can use an inequality to solve it.

Conclusion

In conclusion, inequalities are an essential part of mathematics and are used to compare expressions. By understanding how to determine which statement matches an inequality, you can solve a wide range of problems involving inequalities.

Final Answer

The final answer is: