https://file.aiquickdraw.com/mathbot/file/1727382057141f71ff3sp.jpg

The inequality you uploaded is:

\[
-3x - 5 < 18x - 8 - 13
\]

Let's simplify and solve it step by step.

### Step 1: Simplify both sides
Simplify the right-hand side first by combining like terms:
\[
18x - 8 - 13 = 18x - 21
\]

Now the inequality is:
\[
-3x - 5 < 18x - 21
\]

### Step 2: Move all terms involving \(x\) to one side
Add \(3x\) to both sides to move the \(x\)-terms to the right-hand side:
\[
-5 < 18x + 3x - 21
\]
\[
-5 < 21x - 21
\]

### Step 3: Move constants to the other side
Add \(21\) to both sides to move the constants to the left-hand side:
\[
-5 + 21 < 21x
\]
\[
16 < 21x
\]

### Step 4: Solve for \(x\)
Divide both sides by \(21\) to isolate \(x\):
\[
\frac{16}{21} < x
\]

This is the solution, which can also be written as:
\[
x > \frac{16}{21}
\]

Let me know if you want more details or have any questions!

### Follow-up questions:
1. How do you handle inequalities with negative coefficients differently?
2. Can you convert this solution into a decimal approximation?
3. How would this inequality change if it involved absolute values?
4. What would happen if the inequality sign was reversed?
5. How can you check if your solution is correct?

**Tip:** When dividing or multiplying by a negative number in inequalities, always remember to flip the inequality sign.

Learn how to solve the linear inequality -3x - 5 < 18x - 8 - 13 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequality simplification, transposition of terms, and solving for x. Suitable for students in Grades 8-10.

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