Solve The Following Inequality:$-\frac{1}{2} P \ \textless \ -16$Which Graph Shows The Correct Solution?

**Solve the Inequality: $-\frac{1}{2} p \ \textless \ -16$**

Understanding the Inequality

In this article, we will solve the inequality $-\frac{1}{2} p \ \textless \ -16$ and determine which graph shows the correct solution. To start, let's break down the inequality and understand what it means.

What is an Inequality?

An inequality is a statement that compares two expressions using a mathematical symbol, such as <, >, ≤, or ≥. In this case, the inequality $-\frac{1}{2} p \ \textless \ -16$ states that the expression $-\frac{1}{2} p$ is less than -16.

Solving the Inequality

To solve the inequality, we need to isolate the variable p. We can do this by multiplying both sides of the inequality by -2, which is the reciprocal of -1/2.

-\frac{1}{2} p < -16
\Rightarrow \quad p > 32

Graphing the Solution

Now that we have solved the inequality, we need to determine which graph shows the correct solution. Let's analyze the inequality $p > 32$.

Graph 1: $p > 32$

This graph shows all values of p that are greater than 32. In other words, it shows all values of p that satisfy the inequality $p > 32$.

Graph 2: $p < 32$

This graph shows all values of p that are less than 32. In other words, it shows all values of p that satisfy the inequality $p < 32$.

Graph 3: $p \leq 32$

This graph shows all values of p that are less than or equal to 32. In other words, it shows all values of p that satisfy the inequality $p \leq 32$.

Graph 4: $p \geq 32$

This graph shows all values of p that are greater than or equal to 32. In other words, it shows all values of p that satisfy the inequality $p \geq 32$.

Which Graph Shows the Correct Solution?

Based on the solution to the inequality $p > 32$, we can see that Graph 1 is the only graph that shows the correct solution.

Q&A

Q: What is the solution to the inequality $-\frac{1}{2} p \ \textless \ -16$?

A: The solution to the inequality is $p > 32$.

Q: Which graph shows the correct solution?

A: Graph 1 shows the correct solution.

Q: Why is Graph 1 the correct solution?

A: Graph 1 shows all values of p that are greater than 32, which is the solution to the inequality $p > 32$.

Q: What is the difference between the inequality $p > 32$ and the inequality $p < 32$?

A: The inequality $p > 32$ states that p is greater than 32, while the inequality $p < 32$ states that p is less than 32.

Q: How do you solve an inequality?

A: To solve an inequality, you need to isolate the variable by performing the same operations on both sides of the inequality.

Q: What is the reciprocal of -1/2?

A: The reciprocal of -1/2 is -2.

Q: How do you multiply both sides of an inequality by a negative number?

A: When multiplying both sides of an inequality by a negative number, you need to flip the direction of the inequality sign.

Conclusion

In this article, we solved the inequality $-\frac{1}{2} p \ \textless \ -16$ and determined which graph shows the correct solution. We also answered some common questions about solving inequalities and graphing solutions.