https://file.aiquickdraw.com/mathbot/file/1732627491496t7n9kbya.jpg

 PIL import Image
import pytesseract

# Load the image for text extraction
image_path = "/mnt/data/1732627491496t7n9kbya.jpg"
extracted_text = pytesseract.image_to_string(Image.open(image_path))

# Output the extracted text
extracted_textHere is the extracted text. I will now proceed to solve questions 1–10 from the textbook section.

### 1. Solve \( 8x + 4 = 3(x - 1) + 7 \)
Expand and simplify:
\[
8x + 4 = 3x - 3 + 7
\]
\[
8x + 4 = 3x + 4
\]
\[
8x - 3x = 4 - 4
\]
\[
5x = 0 \quad \Rightarrow \quad x = 0
\]

---

### 2. Solve \( x = \frac{4}{5}(x + 10) \)
Multiply through by 5 to eliminate the denominator:
\[
5x = 4(x + 10)
\]
\[
5x = 4x + 40
\]
\[
5x - 4x = 40
\]
\[
x = 40
\]

---

### 3. Solve \( \frac{2x}{3} + 1 = \frac{7x}{15} + 3 \)
Eliminate fractions by multiplying through by the LCM of 3 and 15 (15):
\[
15 \cdot \frac{2x}{3} + 15 \cdot 1 = 15 \cdot \frac{7x}{15} + 15 \cdot 3
\]
\[
10x + 15 = 7x + 45
\]
\[
10x - 7x = 45 - 15
\]
\[
3x = 30 \quad \Rightarrow \quad x = 10
\]

---

### 4. Solve \( 2y + 5 = \frac{26}{3} - y \)
Multiply through by 3 to eliminate fractions:
\[
3(2y + 5) = 26 - 3y
\]
\[
6y + 15 = 26 - 3y
\]
\[
6y + 3y = 26 - 15
\]
\[
9y = 11 \quad \Rightarrow \quad y = \frac{11}{9}
\]

---

### 5. Solve \( 3m = 5m - \frac{8}{5} \)
Rearrange terms:
\[
3m - 5m = -\frac{8}{5}
\]
\[
-2m = -\frac{8}{5}
\]
\[
m = \frac{8}{10} \quad \Rightarrow \quad m = \frac{4}{5}
\]

---

### 6. Solve \( \frac{8x}{3} - \frac{17}{6} = \frac{5x}{2} \)
Multiply through by 6 to eliminate fractions:
\[
6 \cdot \frac{8x}{3} - 6 \cdot \frac{17}{6} = 6 \cdot \frac{5x}{2}
\]
\[
16x - 17 = 15x
\]
\[
16x - 15x = 17
\]
\[
x = 17
\]

---

### 7. Solve \( \frac{3t - 2}{4} = \frac{2t + 3}{3} = \frac{2}{3} - t \)
Break into two parts:
1. \( \frac{3t - 2}{4} = \frac{2t + 3}{3} \):
\[
3(3t - 2) = 4(2t + 3)
\]
\[
9t - 6 = 8t + 12
\]
\[
9t - 8t = 12 + 6
\]
\[
t = 18
\]
2. \( \frac{3t - 2}{4} = \frac{2}{3} - t \):
\[
3(3t - 2) = 4(2 - 3t)
\]
\[
9t - 6 = 8 - 12t
\]
\[
21t = 14 \quad \Rightarrow \quad t = \frac{2}{3}
\]

---

### 8. Solve \( \frac{m - 1}{2} = 1 - \frac{m - 2}{3} \)
Multiply through by 6 to eliminate fractions:
\[
6 \cdot \frac{m - 1}{2} = 6 \cdot 1 - 6 \cdot \frac{m - 2}{3}
\]
\[
3(m - 1) = 6 - 2(m - 2)
\]
\[
3m - 3 = 6 - 2m + 4
\]
\[
3m + 2m = 6 + 4 + 3
\]
\[
5m = 13 \quad \Rightarrow \quad m = \frac{13}{5}
\]

---

### 9. Solve \( 0.25(4f - 3) = 0.05(10f - 9) \)
Simplify both sides:
\[
(4f - 3) = 0.2(10f - 9)
\]
\[
4f - 3 = 2f - 1.8
\]
\[
4f - 2f = 3 - 1.8
\]
\[
2f = 1.2 \quad \Rightarrow \quad f = 0.6
\]

---

### 10. The sum of three consecutive multiples of 11 is 363.
Let the multiples be \( 11x, 11(x+1), 11(x+2) \):
\[
11x + 11(x + 1) + 11(x + 2) = 363
\]
\[
11(3x + 3) = 363
\]
\[
33x + 33 = 363
\]
\[
33x = 330 \quad \Rightarrow \quad x = 10
\]
Multiples are \( 110, 121, \) and \( 132 \).

---

Would you like detailed explanations for any of the solutions? Let me know! Here are some related questions to practice:

1. How can equations involving fractions be simplified?
2. What strategies help in solving linear equations with multiple variables?
3. How are word problems converted into equations effectively?
4. Can linear equations always be solved with substitution or elimination?
5. What are the key differences between consecutive multiples and consecutive integers?

**Tip:** Always simplify equations step by step to minimize errors.

Explore step-by-step solutions to 10 linear equations, including topics like fractions, algebraic simplifications, and word problems. Perfect for students in Grades 8-10 to master solving linear equations effectively.

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