7. Solve the equation $$ \sqrt[3]{-2 x+5}=-3 $$ for $$ x $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ \sqrt[3]{-2x + 5} = -3 $$ for $$ x $$, follow these steps:

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

$$
   \left( \sqrt[3]{-2x + 5} \right)^3 = (-3)^3
   $$
   
   Simplifying both sides:

$$
   -2x + 5 = -27
   $$

2. **Isolate the Term with $$ x $$:**
   
   Subtract 5 from both sides to isolate the term containing $$ x $$:

$$
   -2x + 5 - 5 = -27 - 5
   $$
   
   Simplifying:

$$
   -2x = -32
   $$

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

$$
   \frac{-2x}{-2} = \frac{-32}{-2}
   $$
   
   Simplifying:

$$
   x = 16
   $$

**Solution:**
$$
x = 16
$$
$$ x = 16 $$

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