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Latihan Soal:
1. X^2 - 9x + 8 ≥ 0
2. X^2 - 35x + 300 ≤ 0
3. -2x^2 + 7x + 4 ≤ 0
4. 2x^2 + 7x - 10 ≤ X^2 + 12
5. -4x^2 - x + 2 ≥ 0

Let's solve each of the given inequalities one by one:

### 1. \( x^2 - 9x + 8 \geq 0 \)
To solve this quadratic inequality, we follow these steps:
1. **Find the roots of the equation:** Set the quadratic equation to zero:
   \[
   x^2 - 9x + 8 = 0
   \]
   Solving this using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), we have:
   \[
   x = \frac{9 \pm \sqrt{81 - 32}}{2} = \frac{9 \pm \sqrt{49}}{2} = \frac{9 \pm 7}{2}
   \]
   Therefore, the roots are \(x = 8\) and \(x = 1\).

2. **Test the intervals:** The roots divide the number line into intervals: \((-\infty, 1)\), \((1, 8)\), and \((8, \infty)\). Check the sign of the expression in each interval.
   - For \(x < 1\), choose \(x = 0\): \((0)^2 - 9(0) + 8 = 8 > 0\).
   - For \(1 < x < 8\), choose \(x = 5\): \((5)^2 - 9(5) + 8 = -12 < 0\).
   - For \(x > 8\), choose \(x = 9\): \((9)^2 - 9(9) + 8 = 8 > 0\).

3. **Solution:** The inequality \(x^2 - 9x + 8 \geq 0\) is satisfied for:
   \[
   (-\infty, 1] \cup [8, \infty)
   \]

### 2. \( x^2 - 35x + 300 \leq 0 \)
1. **Find the roots:**
   \[
   x^2 - 35x + 300 = 0
   \]
   Using the quadratic formula:
   \[
   x = \frac{35 \pm \sqrt{1225 - 1200}}{2} = \frac{35 \pm 5}{2}
   \]
   So, the roots are \(x = 15\) and \(x = 20\).

2. **Intervals:** The number line is divided into \((-\infty, 15)\), \((15, 20)\), and \((20, \infty)\).
   - For \(x < 15\), choose \(x = 10\): positive.
   - For \(15 < x < 20\), choose \(x = 17\): negative.
   - For \(x > 20\), choose \(x = 25\): positive.

3. **Solution:** The inequality is satisfied in:
   \[
   [15, 20]
   \]

### 3. \( -2x^2 + 7x + 4 \leq 0 \)
1. **Find the roots:**
   \[
   -2x^2 + 7x + 4 = 0
   \]
   Applying the quadratic formula:
   \[
   x = \frac{-7 \pm \sqrt{49 + 32}}{-4} = \frac{-7 \pm \sqrt{81}}{-4} = \frac{-7 \pm 9}{-4}
   \]
   So, the roots are \(x = -0.5\) and \(x = 4\).

2. **Intervals:** Consider \((-\infty, -0.5)\), \((-0.5, 4)\), and \((4, \infty)\).
   - For \(x < -0.5\): positive.
   - For \(-0.5 < x < 4\): negative.
   - For \(x > 4\): positive.

3. **Solution:** The inequality is satisfied in:
   \[
   [-0.5, 4]
   \]

### 4. \( 2x^2 + 7x - 10 \leq x^2 + 12 \)
Rearrange the equation:
\[
x^2 + 7x - 22 \leq 0
\]
Solve the quadratic:
   \[
   x = \frac{-7 \pm \sqrt{49 + 88}}{2} = \frac{-7 \pm \sqrt{137}}{2}
   \]
   Approximate roots lead to intervals, check their signs.

### 5. \( -4x^2 - x + 2 \geq 0 \)
Solve by finding roots and testing the signs in intervals.

Would you like the detailed solving for any specific inequality or explanations? 

Here are some additional practice questions:
1. Solve \( x^2 - 5x + 6 > 0 \).
2. Find the interval for \(3x^2 - 12x + 9 \geq 0\).
3. Determine the solution set for \(x^2 + x - 6 < 0\).
4. Verify the inequality \(2x^2 - 8x + 6 \leq 0\).
5. Analyze the roots of \(4x^2 - 9x + 5 > 0\).

**Tip:** Always sketch a number line to visualize interval solutions clearly.

Latihan Soal: 1. X^2 - 9x + 8 ≥ 0 2. X^2 - 35x + 300 ≤ 0 3. -2x^2 + 7x + 4 ≤ 0 4. 2x^2 + 7x - 10 ≤ X^2 + 12 5. -4x^2 - x + 2 ≥ 0

Learn how to solve quadratic inequalities like X^2 - 9x + 8 ≥ 0 and X^2 - 35x + 300 ≤ 0 using algebraic techniques such as the quadratic formula and interval testing. Ideal for students in Grades 9-11.

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