8. Solve the equation $$ \sqrt[3]{7 x+1}=4 $$. What is the value of $$ x $$ ?

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To solve the equation $$ \sqrt[3]{7x + 1} = 4 $$ for $$ x $$, follow these steps:

1. **Isolate the Cube Root:**
   
   The equation is already isolated with the cube root on one side:
   $$
   \sqrt[3]{7x + 1} = 4
   $$

2. **Eliminate the Cube Root by Cubing Both Sides:**
   
   To remove the cube root, cube both sides of the equation:
   $$
   \left( \sqrt[3]{7x + 1} \right)^3 = 4^3
   $$
   
   Simplifying both sides gives:
   $$
   7x + 1 = 64
   $$

3. **Solve for $$ x $$:**
   
   Subtract 1 from both sides to isolate the term with $$ x $$:
   $$
   7x = 64 - 1
   $$
   $$
   7x = 63
   $$
   
   Finally, divide both sides by 7:
   $$
   x = \frac{63}{7} = 9
   $$

**Answer:** The value of $$ x $$ is **9**.
$$ x = 9 $$

8. Solve the equation \( \sqrt[3]{7 x+1}=4 \). What is the value of \( x \) ?

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