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

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

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

Answer 5

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.