What Number Could Replace $x$ To Make A True Statement?$\frac{2}{3}\ \textless \ \frac{x}{8}\ \textless \ \frac{7}{8}$A. 3 B. 4 C. 5 D. 6

What Number Could Replace $x$ to Make a True Statement?

In mathematics, inequalities are used to compare the values of different expressions. A true statement is one that is logically correct and consistent with the given information. In this article, we will explore the concept of inequalities and how to find a number that can replace $x$ to make a true statement.

An inequality is a statement that compares two expressions using a mathematical symbol, such as $<$, $>$, $\leq$, or $\geq$. Inequalities can be used to describe relationships between variables, constants, or expressions. For example, the inequality $\frac{2}{3} < \frac{x}{8}$ states that the value of $\frac{x}{8}$ is greater than $\frac{2}{3}$.

The given inequality is $\frac{2}{3} < \frac{x}{8} < \frac{7}{8}$. This inequality states that the value of $\frac{x}{8}$ is greater than $\frac{2}{3}$ and less than $\frac{7}{8}$. To find a number that can replace $x$ to make this statement true, we need to find a value of $x$ that satisfies both inequalities.

To solve the inequality, we can start by multiplying both sides of the inequality by 8, which is the denominator of the fraction $\frac{x}{8}$. This gives us:

$$16 < x < 56$$

This inequality states that the value of $x$ is greater than 16 and less than 56.

Now that we have the inequality $16 < x < 56$, we can look at the answer choices to see which one satisfies this inequality. The answer choices are:

A. 3 B. 4 C. 5 D. 6

We can see that none of these answer choices satisfy the inequality $16 < x < 56$. However, we can try to find a number that is close to the answer choices and satisfies the inequality.

Let's analyze each answer choice to see if it satisfies the inequality $16 < x < 56$.

• A. 3: This value is less than 16, so it does not satisfy the inequality.
• B. 4: This value is also less than 16, so it does not satisfy the inequality.
• C. 5: This value is still less than 16, so it does not satisfy the inequality.
• D. 6: This value is greater than 16, but it is not less than 56, so it does not satisfy the inequality.

Since none of the answer choices satisfy the inequality $16 < x < 56$, we need to look for a number that is between 16 and 56. Let's try to find a number that is close to the midpoint of this range.

The midpoint of the range 16 to 56 is:

$$\frac{16 + 56}{2} = 36$$

This value is between 16 and 56, so it satisfies the inequality $16 < x < 56$.

In conclusion, the correct answer is not among the answer choices A, B, C, or D. However, we can find a number that satisfies the inequality $16 < x < 56$ by finding the midpoint of this range. The midpoint is 36, which is the correct answer.

The final answer is $\boxed{36}$.
What Number Could Replace $x$ to Make a True Statement? - Q&A

In our previous article, we explored the concept of inequalities and how to find a number that can replace $x$ to make a true statement. We analyzed the given inequality $\frac{2}{3} < \frac{x}{8} < \frac{7}{8}$ and found that the correct answer is 36. In this article, we will answer some frequently asked questions related to this topic.

Q: What is an inequality?

A: An inequality is a statement that compares two expressions using a mathematical symbol, such as $<$, $>$, $\leq$, or $\geq$. Inequalities can be used to describe relationships between variables, constants, or expressions.

Q: How do I solve an inequality?

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

Q: What is the difference between $<$ and $\leq$?

A: The symbol $<$ means "less than", while the symbol $\leq$ means "less than or equal to". For example, the inequality $x < 5$ means that $x$ is less than 5, while the inequality $x \leq 5$ means that $x$ is less than or equal to 5.

Q: How do I find the midpoint of a range?

A: To find the midpoint of a range, you can add the two endpoints of the range together and divide by 2. For example, the midpoint of the range 16 to 56 is:

$$\frac{16 + 56}{2} = 36$$

Q: Why is the midpoint of a range important?

A: The midpoint of a range is important because it can help you find a value that satisfies an inequality. By finding the midpoint of a range, you can determine if a value is within the range or not.

Q: Can I use the midpoint of a range to find a value that satisfies an inequality?

A: Yes, you can use the midpoint of a range to find a value that satisfies an inequality. By finding the midpoint of a range, you can determine if a value is within the range or not. However, you should also check the endpoints of the range to make sure that the value satisfies the inequality.

Q: What if the inequality has multiple variables?

A: If the inequality has multiple variables, you can use the same methods to solve the inequality as you would with a single variable. However, you may need to use more complex methods, such as substitution or elimination, to solve the inequality.

In conclusion, inequalities are an important concept in mathematics that can be used to describe relationships between variables, constants, or expressions. By understanding how to solve inequalities and find the midpoint of a range, you can determine if a value satisfies an inequality or not. We hope that this article has been helpful in answering your questions about inequalities.

• Always read the problem carefully and understand what is being asked.
• Use the correct methods to solve the inequality, such as substitution or elimination.
• Check the endpoints of the range to make sure that the value satisfies the inequality.
• Use the midpoint of a range to find a value that satisfies an inequality.

• Khan Academy: Inequalities
• Mathway: Inequalities
• Wolfram Alpha: Inequalities

We hope that this article has been helpful in answering your questions about inequalities. If you have any further questions, please don't hesitate to ask.