To place the inequality $y^2 < y$ into a position where it holds true, such as around $y = -2$, you need to check if $y = -2$ satisfies the inequality. Here's how you do it:

1. Start with the inequality: $y^2 < y$

2. Substitute $y = -2$ into the inequality: $(-2)^2 < -2$

3. Simplify both sides: $4 < -2$

Since $4$ is not less than $-2$, the inequality $y^2 < y$ does not hold true at $y = -2$.

To find where the inequality holds, let's analyze it further:

1. Rearrange the inequality: $y^2 - y < 0$

2. Factor the expression: $y(y - 1) < 0$

This inequality holds where the product $y(y - 1)$ is negative, which occurs between the roots $y = 0$ and $y = 1$. Thus, $y$ must lie in the interval $0 < y < 1$.

Steps Summary:

• Check if a specific value like $y = -2$ satisfies the inequality by substituting and simplifying.
• Analyze and factor the inequality to find the range of $y$ where the inequality holds.

Would you like more details on analyzing inequalities or have any questions?

Here are some related questions:

1. How do you solve quadratic inequalities?
2. What does it mean when the inequality sign changes direction?
3. How can you graph the solution to an inequality?
4. What are common methods for factoring quadratic expressions?
5. How do you test if a specific value satisfies an inequality?

Tip: Always check the roots and intervals around them when solving inequalities involving polynomials.