Why the correct answer of this question is 7 while I always find 3 as the minimum value instead of 7? The picture includes two different solutions.

see below

Step-by-step explanation:

This solution is based off of the Triangle Inequality, which states that the sum of the two shortest sides of a triangle must be greater than the longest side of the triangle. The solution looks at the diagram on the bottom where y = DB. Looking at ΔABD, to find the range of values for y, we must consider two possible cases: y is either the shortest side or the longest side. If y is the shortest side then y + 5 > 6 which means y > 1 and if y is the longest side then 6 + 5 > y which means 11 > y. Therefore, the range of values for y is 1 < y < 11.

Next, they made y as small as possible, which would be 1.1 in this case. Looking at ΔDCB, again, to find the range of values for x, we must consider two possible cases: x is either one of the shortest sides or x is the longest side. If x is one of the shorter sides then 1.1 + x > 8 so x > 6.9 and if x is the longest side, 1.1 + 8 > x so 9.1 > x. Therefore, the range of values for x is 6.9 < x < 9.1. The smallest integer value that satisfies this inequality is x = 7.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

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step-by-step explanation: