https://file.aiquickdraw.com/mathbot/file/1730438615169ks4p3om8.jpg

Let's solve each equation for \( x \) and explain the steps.

### Part (a)
**Equation:**  
\[
\frac{x}{8} = \frac{3}{4}
\]

**Solution:**  
1. To eliminate the fraction, multiply both sides by 8:
   \[
   x = 8 \cdot \frac{3}{4}
   \]
2. Simplify the right side:
   \[
   x = \frac{24}{4} = 6
   \]

**Answer:**  
\[
x = 6
\]

---

### Part (b)
**Equation:**  
\[
5x - (x + 1) = 5 - 2x
\]

**Solution:**  
1. Distribute the negative sign on the left side:
   \[
   5x - x - 1 = 5 - 2x
   \]
2. Simplify by combining like terms:
   \[
   4x - 1 = 5 - 2x
   \]
3. Add \( 2x \) to both sides to get all terms involving \( x \) on one side:
   \[
   6x - 1 = 5
   \]
4. Add 1 to both sides:
   \[
   6x = 6
   \]
5. Divide by 6:
   \[
   x = 1
   \]

**Answer:**  
\[
x = 1
\]

---

### Part (c)
**Equation:**  
\[
3x + 5 - x = x - 3
\]

**Solution:**  
1. Combine like terms on the left side:
   \[
   2x + 5 = x - 3
   \]
2. Subtract \( x \) from both sides:
   \[
   x + 5 = -3
   \]
3. Subtract 5 from both sides:
   \[
   x = -8
   \]

**Answer:**  
\[
x = -8
\]

---

### Part (d)
**Equation:**  
\[
\frac{2}{5} = \frac{x}{40}
\]

**Solution:**  
1. To clear the fraction, multiply both sides by 40:
   \[
   40 \cdot \frac{2}{5} = x
   \]
2. Simplify the left side:
   \[
   x = \frac{80}{5} = 16
   \]

**Answer:**  
\[
x = 16
\]

---

Let me know if you have any questions or would like further details.

### Related Questions:
1. How can you verify the solution to an equation once you have solved it?
2. What is the effect of multiplying both sides of an equation by a number?
3. Can you solve an equation with variables on both sides in a different way?
4. How can simplifying an equation help in solving it?
5. Why is it important to perform the same operation on both sides of an equation?

### Tip:
When solving equations with fractions, consider clearing the fractions by multiplying both sides by the least common multiple of the denominators.

Solve each equation for x: (a) x/8 = 3/4, (b) 5x - (x + 1) = 5 - 2x, (c) 3x + 5 - x = x - 3, (d) 2/5 = x/40. Explain or justify each step.

Step-by-step solutions for solving equations involving fractions and variables on both sides. Learn how to solve equations like x/8 = 3/4, 5x - (x + 1) = 5 - 2x, and more. This guide is perfect for middle school students in Grades 6-8.

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