Final answer:
To find the solution to the equation 7 - ∛(2-x) = 12, we subtract 7 from both sides, cube both sides, then solve for x, finding that x = -123.
Step-by-step explanation:
The student's question is asking for the solution to the equation 7 - ∛(2-x) = 12. To solve for x, we'll first isolate the cube root term by subtracting 7 from both sides of the equation, giving us ∛(2-x) = 5. We then cube both sides to eliminate the cube root, resulting in 2 - x = 125. Now, we solve for x by subtracting 125 from both sides and multiplying by -1, which gives us x = -123.
Here is the step-by-step solution: