9. Solve the equation $$ \sqrt[3]{2 x+1}+3=5 $$. What is the value of $$ x $$ ?

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\sqrt[3]{2x + 1} + 3 = 5
$$

follow these steps:

1. **Isolate the Cube Root:**
   
   Subtract 3 from both sides of the equation to isolate the cube root term.

$$
   \sqrt[3]{2x + 1} = 5 - 3
   $$
   
   $$
   \sqrt[3]{2x + 1} = 2
   $$

2. **Eliminate the Cube Root:**
   
   To remove the cube root, cube both sides of the equation.

$$
   \left( \sqrt[3]{2x + 1} \right)^3 = 2^3
   $$
   
   $$
   2x + 1 = 8
   $$

3. **Solve for $$ x $$:**
   
   - **Subtract 1** from both sides:

$$
     2x = 8 - 1
     $$
     
     $$
     2x = 7
     $$

- **Divide** both sides by 2 to solve for $$ x $$:

$$
     x = \frac{7}{2}
     $$
     
     $$
     x = 3.5
     $$

**Final Answer:**

$$
x = \frac{7}{2} \quad \text{or} \quad x = 3.5
$$
$$ x = \frac{7}{2} $$ or $$ x = 3.5 $$

9. Solve the equation \( \sqrt[3]{2 x+1}+3=5 \). What is the value of \( x \) ?