Let's solve the inequality:

\[
-5(x - 6) < -3(x + 7) + x
\]

### Step 1: Expand both sides of the inequality

On the left-hand side:
\[
-5(x - 6) = -5x + 30
\]

On the right-hand side:
\[
-3(x + 7) + x = -3x - 21 + x = -2x - 21
\]

Now the inequality is:
\[
-5x + 30 < -2x - 21
\]

### Step 2: Combine like terms

Add \(5x\) to both sides:
\[
30 < 3x - 21
\]

### Step 3: Isolate \(x\)

Add 21 to both sides:
\[
30 + 21 < 3x
\]
\[
51 < 3x
\]

### Step 4: Solve for \(x\)

Divide both sides by 3:
\[
x > 17
\]

### Final Solution:
\[
x > 17
\]

This means that the solution to the inequality is \(x > 17\).

---

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How do you solve similar inequalities with fractions?
2. What happens if you multiply or divide by a negative number in an inequality?
3. How do you check if a solution satisfies an inequality?
4. Can inequalities have multiple solution sets?
5. What are the rules for combining inequalities?

**Tip:** Always reverse the inequality sign when multiplying or dividing by a negative number!

Discover how to solve the linear inequality -5(x - 6) < -3(x + 7) + x with a step-by-step guide. This solution covers important algebraic concepts including the expansion of brackets and properties of inequalities, tailored for students in Grades 8-10.

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