https://file.aiquickdraw.com/mathbot/file/1728752628877usqyjxgm.jpg

The inequality given in the image is:

\[
2x - 1 < \frac{-2 - x}{-3}
\]

### Step 1: Simplify the right-hand side
First, simplify the right-hand side. We have:

\[
\frac{-2 - x}{-3} = \frac{-1(-2 - x)}{-1(-3)} = \frac{2 + x}{3}
\]

So the inequality becomes:

\[
2x - 1 < \frac{2 + x}{3}
\]

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply both sides of the inequality by 3:

\[
3(2x - 1) < 2 + x
\]

Simplifying both sides:

\[
6x - 3 < 2 + x
\]

### Step 3: Isolate the variable
Now, subtract \(x\) from both sides:

\[
6x - x - 3 < 2
\]

This simplifies to:

\[
5x - 3 < 2
\]

Next, add 3 to both sides:

\[
5x < 5
\]

Finally, divide by 5:

\[
x < 1
\]

### Step 4: Solution set in interval notation
The solution is \(x < 1\), which in interval notation is:

\[
(-\infty, 1)
\]

Would you like further clarification on any of these steps or additional details?

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Here are some related questions to explore:
1. How do you solve an inequality involving absolute values?
2. What are the properties of inequalities when multiplying or dividing by negative numbers?
3. How do you graph a linear inequality on a number line?
4. How do you solve compound inequalities?
5. What changes when an inequality includes a "greater than or equal to" symbol?

**Tip:** When solving inequalities, remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.

Solve the inequality symbolically: 2x - 1 < (-2 - x) / -3. Express the solution set in interval notation.

Learn how to solve the linear inequality 2x - 1 < (-2 - x) / -3 with step-by-step guidance. This problem involves simplifying fractions, eliminating denominators, and solving for x. Suitable for high school students in Grades 9-11.

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