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Let's break down and solve the inequalities one by one.

### 9) \( x \lt \frac{1}{4}(3x + 4) \)

1. Multiply both sides of the inequality by 4 to eliminate the fraction:
   \[
   4x \lt 3x + 4
   \]

2. Subtract \(3x\) from both sides:
   \[
   4x - 3x \lt 4
   \]
   Simplifying gives:
   \[
   x \lt 4
   \]

Thus, the solution to the inequality is:
\[
x \lt 4
\]

---

### 10) \( 2(x + 4) \leq 3(x + 7) - 4 \)

1. Expand both sides:
   \[
   2(x + 4) = 2x + 8
   \]
   \[
   3(x + 7) - 4 = 3x + 21 - 

Solve the following inequalities:
1) x < 1/4(3x + 4)
2) 2(x + 4) ≤ 3(x + 7) - 4

Learn how to solve inequalities such as x < 1/4(3x + 4) and 2(x + 4) ≤ 3(x + 7) - 4 step-by-step. This problem covers key algebra concepts like linear inequalities, distributive property, and transposing terms, suitable for students in Grades 9-10.

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