A number n is increased by 8. If the cube root of that results equals - 0.5, what is the value of n?

The cube root of (n increased by 8), or ∛ (n+8), is - 0.5, or - 1/2.

∛ (n+8) = - 1/2. To solve this for n, cube both sides, obtaining n+8 = - 1/8.

Eliminate the fraction by mult. all three terms by 8: 8n + 64 = - 1

Solving for n: 8n = - 65, so that n = - 65/8.