To solve the inequality \( 7x + 6 < 17 - 3x \), follow these steps:

### Step 1: Combine like terms
Move all the terms involving \( x \) to one side, and constants to the other side.

\[
7x + 3x < 17 - 6
\]

This simplifies to:

\[
10x < 11
\]

### Step 2: Solve for \( x \)
Now, divide both sides of the inequality by 10 to isolate \( x \).

\[
x < \frac{11}{10}
\]

Thus, the solution is:

\[
x < 1.1
\]

### Final Answer:
\[
x < 1.1
\]

Would you like more details on any step or have questions?

Here are 5 related questions for practice:
1. Solve: \( 4x + 5 < 15 - 2x \)
2. Solve: \( 5x - 4 \leq 12 + x \)
3. Solve: \( 6x + 3 > 2x + 7 \)
4. Solve: \( 8x + 7 > 5x + 12 \)
5. Solve: \( 3x + 8 \geq 2x + 14 \)

**Tip**: When solving inequalities, remember to reverse the inequality sign if you multiply or divide by a negative number!

Learn how to solve the linear inequality 7x + 6 < 17 - 3x step-by-step. This problem demonstrates combining like terms and solving inequalities by isolating variables. It is ideal for students in Grades 8-10.

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