Solve the equation. $$ \begin{array}{c}\sqrt[3]{2 x+6}-1=3 \ x=[?]\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\sqrt[3]{2x + 6} - 1 = 3
$$

follow these steps:

1. **Isolate the Cube Root:**

$$
   \sqrt[3]{2x + 6} = 3 + 1
   $$
   
   $$
   \sqrt[3]{2x + 6} = 4
   $$

2. **Eliminate the Cube Root by Cubing Both Sides:**

$$
   \left(\sqrt[3]{2x + 6}\right)^3 = 4^3
   $$
   
   $$
   2x + 6 = 64
   $$

3. **Solve for $$ x $$:**

- Subtract 6 from both sides:

$$
     2x = 64 - 6
     $$
     
     $$
     2x = 58
     $$
     
   - Divide both sides by 2:

$$
     x = \frac{58}{2}
     $$
     
     $$
     x = 29
     $$

**Solution:** $$ x = 29 $$
$$ x = 29 $$

Solve the equation. \( \begin{array}{c}\sqrt[3]{2 x+6}-1=3 \\ x=[?]\end{array} \)