Solve the one-variable inequality x−91<18 .

To solve the inequality \( x - 91 < 18 \), we will isolate \( x \).

1. Start by adding 91 to both sides of the inequality:

\[
x - 91 + 91 < 18 + 91
\]

2. This simplifies to:

\[
x < 109
\]

So, the solution to the inequality is:

\[
x < 109
\]

This means that \( x \) can take on any value that is less than 109.

Solve the one-variable inequality 3/5x>9 .

To solve the inequality \(\frac{3}{5}x > 9\), follow these steps:

1. **Multiply both sides by 5** to eliminate the fraction:

\[
5 \cdot \frac{3}{5}x > 5 \cdot 9
\]

This simplifies to:

\[
3x > 45
\]

2. **Divide both sides by 3** to isolate \(x\):

\[
\frac{3x}{3} > \frac{45}{3}
\]

This simplifies to:

\[
x > 15
\]

Thus, the solution to the inequality is:

\[
x > 15
\]

This means that \(x\) can take any value greater than 15.

What solution set would you graph with a closed circle at −9.5 and a ray extending to the left

A closed circle at \(-9.5\) indicates that the value \(-9.5\) is included in the solution set. A ray extending to the left signifies that the values less than \(-9.5\) are included.

Therefore, the solution set can be expressed in interval notation as:

\[
(-\infty, -9.5]
\]

This means any value less than or equal to \(-9.5\) is included in the solution set. The closed circle indicates that \(-9.5\) itself is part of the solution.