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The given inequality is:

\[
2(2x + 1.5) < 18 - x
\]

Let's solve the inequality step-by-step:

1. **Expand the left-hand side:**

\[
2(2x + 1.5) = 4x + 3
\]

Thus, the inequality becomes:

\[
4x + 3 < 18 - x
\]

2. **Add \( x \) to both sides** to eliminate \( -x \) on the right-hand side:

\[
4x + 3 + x < 18
\]

Simplifying:

\[
5x + 3 < 18
\]

3. **Subtract 3 from both sides**:

\[
5x < 15
\]

4. **Divide by 5**:

\[
x < 3
\]

The solution is:

\[
x < 3
\]

Would you like to see a detailed breakdown of the solution, or do you have any questions? Here are some related questions to consider:

1. What is the effect of multiplying or dividing both sides of an inequality by a negative number?
2. How would the solution change if the inequality symbol were reversed?
3. What are common strategies for solving compound inequalities?
4. How do you check if a solution satisfies the original inequality?
5. What is the graphical representation of the solution \( x < 3 \) on a number line?

**Tip:** When solving inequalities, always be mindful of how the inequality sign changes when multiplying or dividing by a negative value.

Learn how to solve the linear inequality 2(2x + 1.5) < 18 - x with a step-by-step breakdown. This problem covers algebraic concepts, including expanding brackets and simplifying inequalities, ideal for students in Grades 7-9.

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