https://r2.erweima.ai/mathbot/image/17260561793233ci7znsp.jpg

The image contains multiple compound inequalities that we will solve one by one. Let's go through each of them systematically:

### e) \( 5 \leq 35x - 10 \leq 15 \)

**Step 1:** Add 10 to all sides to isolate the term with \( x \).
\[ 5 + 10 \leq 35x - 10 + 10 \leq 15 + 10 \]
\[ 15 \leq 35x \leq 25 \]

**Step 2:** Divide all parts by 35 to solve for \( x \).
\[ \frac{15}{35} \leq x \leq \frac{25}{35} \]
\[ \frac{3}{7} \leq x \leq \frac{5}{7} \]

### f) \( -1 \geq 3x - 7 > 8 \)

This inequality seems to have a logical issue since \( -1 \) is not greater than 8. Thus, it might be a typographical error or requires rechecking.

### g) \( 6 > 9x + 3 - 15 \)

**Step 1:** Simplify the expression.
\[ 6 > 9x - 12 \]

**Step 2:** Add 12 to both sides.
\[ 18 > 9x \]

**Step 3:** Divide by 9.
\[ 2 > x \text{ or } x < 2 \]

### h) \( 2 \leq 10 - 4x \leq 6 \)

**Step 1:** Subtract 10 from all sides.
\[ 2 - 10 \leq -4x \leq 6 - 10 \]
\[ -8 \leq -4x \leq -4 \]

**Step 2:** Divide by -4 and reverse inequalities (since dividing by a negative).
\[ 2 \geq x \geq 1 \]
\[ 1 \leq x \leq 2 \]

### i) \( 4 < 8x - 28 < 12 \)

**Step 1:** Add 28 to all parts.
\[ 4 + 28 < 8x < 12 + 28 \]
\[ 32 < 8x < 40 \]

**Step 2:** Divide by 8.
\[ 4 < x < 5 \]

If you have any questions or need further details, please let me know! Here are some related topics you might find interesting:
1. How to solve quadratic inequalities?
2. What are the steps to graph a compound inequality on a number line?
3. How do absolute value inequalities differ from linear inequalities?
4. Can compound inequalities have no solution, and how can we identify such cases?
5. What methods are used to solve inequalities involving fractions or decimals?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.

Solve the following compound inequalities: 5 ≤ 35x - 10 ≤ 15, -1 ≥ 3x - 7 > 8, 6 > 9x + 3 > -15, 2 ≤ 10 - 4x ≤ 6, 4 < 8x - 28 < 12

Learn to solve compound inequalities like 5 ≤ 35x - 10 ≤ 15 and 4 < 8x - 28 < 12 with detailed steps. This guide covers essential algebra concepts, key formulas, and inequality rules. Ideal for Grades 9-11.

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