To solve the equation "one fifth times quantity x plus 21 end quantity equals negative 6," we can follow these steps:
1. First, let's translate the given sentence into an equation. The phrase "one fifth times" means multiplying by 1/5, so the equation becomes (1/5)(x + 21) = -6.
2. To solve for x, we need to isolate it on one side of the equation. To do this, we can multiply both sides of the equation by 5, which cancels out the 1/5 coefficient on the left side. This gives us (1/5)(x + 21) * 5 = -6 * 5.
3. Simplifying the equation, we have (x + 21) = -30. Now, we need to get rid of the 21 on the left side to isolate x. We can do this by subtracting 21 from both sides of the equation: (x + 21) - 21 = -30 - 21.
4. Simplifying further, we have x = -51. Therefore, the correct answer is x = -51.
In summary, the correct value for x in the equation (1/5)(x + 21) = -6 is x = -51.