Select The Values That Make The Inequality $-2y \ \textgreater \ 4$ True. Then Write An Equivalent Inequality In Terms Of $y$. (Numbers Are Written In Order From Least To Greatest Across.)Options:-12, -7, -5, -3, -2, -1, 1, 3,

Understanding the Inequality

In this section, we will focus on solving the inequality $-2y > 4$. To begin, let's break down the inequality and understand what it means. The inequality states that the product of $-2$ and $y$ is greater than $4$. This means that we are looking for values of $y$ that make the inequality true.

Step 1: Isolate the Variable

To solve the inequality, we need to isolate the variable $y$. We can do this by dividing both sides of the inequality by $-2$. However, when we divide by a negative number, we need to reverse the direction of the inequality sign. So, the inequality becomes:

$$y < -2$$

Step 2: Write the Equivalent Inequality

Now that we have isolated the variable, we can write the equivalent inequality in terms of $y$. The inequality $y < -2$ means that $y$ is less than $-2$. This can be written as:

$$y \in (-\infty, -2)$$

Step 3: Select the Values that Make the Inequality True

Now that we have the equivalent inequality, we can select the values that make the inequality true. The inequality $y < -2$ is true for all values of $y$ that are less than $-2$. Therefore, the values that make the inequality true are:

• -12: This value is less than $-2$, so it makes the inequality true.
• -7: This value is less than $-2$, so it makes the inequality true.
• -5: This value is less than $-2$, so it makes the inequality true.
• -3: This value is less than $-2$, so it makes the inequality true.
• -2: This value is not less than $-2$, so it does not make the inequality true.
• -1: This value is not less than $-2$, so it does not make the inequality true.
• 1: This value is not less than $-2$, so it does not make the inequality true.
• 3: This value is not less than $-2$, so it does not make the inequality true.

Conclusion

Q: What is an inequality?

A: An inequality is a statement that two expressions are not equal. It can be written in the form of $a > b$, $a < b$, $a \geq b$, or $a \leq b$.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. You can do this by adding, subtracting, multiplying, or dividing both sides of the inequality by the same value.

Q: What is the difference between solving an inequality and solving an equation?

A: Solving an equation means finding the value of the variable that makes the equation true. Solving an inequality means finding the set of values of the variable that make the inequality true.

Q: How do I determine the direction of the inequality sign?

A: When you multiply or divide both sides of an inequality by a negative number, you need to reverse the direction of the inequality sign. For example, if you have the inequality $x > 2$ and you multiply both sides by $-1$, the inequality becomes $x < -2$.

Q: What is the concept of "less than" and "greater than" in inequalities?

A: In inequalities, "less than" means that the value on the left side of the inequality sign is smaller than the value on the right side. "Greater than" means that the value on the left side of the inequality sign is larger than the value on the right side.

Q: How do I write the solution to an inequality in interval notation?

A: To write the solution to an inequality in interval notation, you need to determine the set of values that make the inequality true. For example, if the inequality is $x < 2$, the solution in interval notation is $(-\infty, 2)$.

Q: What is the concept of "union" and "intersection" in inequalities?

A: In inequalities, the union of two sets means that the solution is the combination of the two sets. The intersection of two sets means that the solution is the set of values that are common to both sets.

Q: How do I solve a compound inequality?

A: To solve a compound inequality, you need to solve each inequality separately and then combine the solutions. For example, if you have the compound inequality $x > 2$ and $x < 4$, the solution is $x \in (2, 4)$.

Q: What is the concept of "absolute value" in inequalities?

A: In inequalities, the absolute value of a number means its distance from zero on the number line. For example, the absolute value of $-3$ is $3$.

Q: How do I solve an inequality with absolute value?

A: To solve an inequality with absolute value, you need to consider two cases: one where the expression inside the absolute value is positive, and one where the expression inside the absolute value is negative. For example, if you have the inequality $|x| < 2$, the solution is $x \in (-2, 2)$.

Conclusion

In conclusion, solving inequalities requires a deep understanding of the concepts of inequalities, variables, and operations. By following the steps outlined in this article, you can solve inequalities and write the solution in interval notation. Remember to always consider the direction of the inequality sign and the concept of "less than" and "greater than" when solving inequalities.