Math Problems For 8Th Graders With Answers - Free Printable

To solve the given linear equations, we will go through each section step by step. Here's a detailed explanation for solving some of the equations from each section.

---

Section A

#### 1. Solve \( \frac{2x + 5}{3} = 11 \)

1. Eliminate the denominator by multiplying both sides by 3:
\[
2x + 5 = 33
\]
2. Subtract 5 from both sides:
\[
2x = 28
\]
3. Divide by 2:
\[
x = 14
\]

Answer: \( x = 14 \)

---

#### 2. Solve \( \frac{8 - 3x}{2} = 5 \)

1. Eliminate the denominator by multiplying both sides by 2:
\[
8 - 3x = 10
\]
2. Subtract 8 from both sides:
\[
-3x = 2
\]
3. Divide by -3:
\[
x = -\frac{2}{3}
\]

Answer: \( x = -\frac{2}{3} \)

---

#### 3. Solve \( \frac{5 - 9x}{6} = -2 \)

1. Eliminate the denominator by multiplying both sides by 6:
\[
5 - 9x = -12
\]
2. Subtract 5 from both sides:
\[
-9x = -17
\]
3. Divide by -9:
\[
x = \frac{17}{9}
\]

Answer: \( x = \frac{17}{9} \)

---

#### 4. Solve \( \frac{7x + 6}{3} - 9 = -12 \)

1. Add 9 to both sides:
\[
\frac{7x + 6}{3} = -3
\]
2. Eliminate the denominator by multiplying both sides by 3:
\[
7x + 6 = -9
\]
3. Subtract 6 from both sides:
\[
7x = -15
\]
4. Divide by 7:
\[
x = -\frac{15}{7}
\]

Answer: \( x = -\frac{15}{7} \)

---

Section B

#### 1. Solve \( 4(2x - 3) = 8(2x + 5) \)

1. Distribute on both sides:
\[
8x - 12 = 16x + 40
\]
2. Subtract \( 8x \) from both sides:
\[
-12 = 8x + 40
\]
3. Subtract 40 from both sides:
\[
-52 = 8x
\]
4. Divide by 8:
\[
x = -\frac{52}{8} = -\frac{13}{2}
\]

Answer: \( x = -\frac{13}{2} \)

---

#### 2. Solve \( 3(4x - 5) = 5(2x - 5) \)

1. Distribute on both sides:
\[
12x - 15 = 10x - 25
\]
2. Subtract \( 10x \) from both sides:
\[
2x - 15 = -25
\]
3. Add 15 to both sides:
\[
2x = -10
\]
4. Divide by 2:
\[
x = -5
\]

Answer: \( x = -5 \)

---

#### 3. Solve \( 8(6x + 2) = 5(x - 2) \)

1. Distribute on both sides:
\[
48x + 16 = 5x - 10
\]
2. Subtract \( 5x \) from both sides:
\[
43x + 16 = -10
\]
3. Subtract 16 from both sides:
\[
43x = -26
\]
4. Divide by 43:
\[
x = -\frac{26}{43}
\]

Answer: \( x = -\frac{26}{43} \)

---

Section C

#### 1. Solve \( \frac{5x - 2}{3} = \frac{4x + 1}{2} \)

1. Eliminate the denominators by cross-multiplying:
\[
2(5x - 2) = 3(4x + 1)
\]
2. Distribute on both sides:
\[
10x - 4 = 12x + 3
\]
3. Subtract \( 10x \) from both sides:
\[
-4 = 2x + 3
\]
4. Subtract 3 from both sides:
\[
-7 = 2x
\]
5. Divide by 2:
\[
x = -\frac{7}{2}
\]

Answer: \( x = -\frac{7}{2} \)

---

#### 2. Solve \( \frac{7x}{5} = \frac{2x + 5}{4} \)

1. Eliminate the denominators by cross-multiplying:
\[
4(7x) = 5(2x + 5)
\]
2. Distribute on both sides:
\[
28x = 10x + 25
\]
3. Subtract \( 10x \) from both sides:
\[
18x = 25
\]
4. Divide by 18:
\[
x = \frac{25}{18}
\]

Answer: \( x = \frac{25}{18} \)

---

Final Answer:

\[
\boxed{x = 14, x = -\frac{2}{3}, x = \frac{17}{9}, x = -\frac{15}{7}, x = -\frac{13}{2}, x = -5, x = -\frac{26}{43}, x = -\frac{7}{2}, x = \frac{25}{18}}
\]

(Note: This is a partial solution. You can follow the same steps to solve the remaining equations in Sections A, B, and C.)