Consider The Following Inequality:$\[ -10 \ \textgreater \ -\frac{5}{6} P \\]1. Solve The Inequality For \[$p\$\].2. Graph The Solution.

**Solving and Graphing the Inequality: A Step-by-Step Guide**

What is the Given Inequality?

The given inequality is $-10 \ \textgreater \ -\frac{5}{6} p$. This means that the value of $-10$ is greater than the value of $-\frac{5}{6} p$.

How to Solve the Inequality for $p$?

To solve the inequality for $p$, we need to isolate the variable $p$ on one side of the inequality sign. Here are the steps:

Step 1: Multiply Both Sides by -6

To get rid of the fraction, we can multiply both sides of the inequality by $-6$. This will give us:

$$-10 \times -6 \ \textgreater \ -\frac{5}{6} p \times -6$$

Simplifying the left-hand side, we get:

$$60 \ \textgreater \ 5p$$

Step 2: Divide Both Sides by 5

To isolate the variable $p$, we can divide both sides of the inequality by $5$. This will give us:

$$\frac{60}{5} \ \textgreater \ p$$

Simplifying the left-hand side, we get:

$$12 \ \textgreater \ p$$

Step 3: Write the Solution in Interval Notation

The solution to the inequality is $p < 12$. We can write this in interval notation as $(-\infty, 12)$.

Q: What is the solution to the inequality?

A: The solution to the inequality is $p < 12$, which can be written in interval notation as $(-\infty, 12)$.

Q: How do I graph the solution?

A: To graph the solution, we can draw a number line and shade the region to the left of $12$. This represents all the values of $p$ that satisfy the inequality.

Q: What is the meaning of the inequality?

A: The inequality $p < 12$ means that the value of $p$ is less than $12$. In other words, $p$ can take on any value that is less than $12$.

Q: Can I use this inequality to solve for $p$ in a different equation?

A: Yes, you can use this inequality to solve for $p$ in a different equation. For example, if you have the equation $2p + 5 = 25$, you can use the inequality to find the value of $p$.

Q: How do I know if the inequality is true or false?

A: To determine if the inequality is true or false, you can plug in a value of $p$ into the inequality and see if it is true or false. For example, if you plug in $p = 10$, the inequality becomes $10 < 12$, which is true.

Q: Can I use this inequality to solve for $p$ in a system of equations?

A: Yes, you can use this inequality to solve for $p$ in a system of equations. For example, if you have the system of equations $2p + 5 = 25$ and $p - 3 = 2$, you can use the inequality to find the value of $p$.

Q: How do I know if the inequality is an equality or an inequality?

A: To determine if the inequality is an equality or an inequality, you can look at the inequality sign. If the inequality sign is $>$, it means that the inequality is strict, and if the inequality sign is $\geq$, it means that the inequality is non-strict.

Q: Can I use this inequality to solve for $p$ in a quadratic equation?

A: Yes, you can use this inequality to solve for $p$ in a quadratic equation. For example, if you have the quadratic equation $p^2 + 4p + 4 = 0$, you can use the inequality to find the value of $p$.