Question

Find the solution set of each of the following inequations in the given domain.

Answer 1

Answer:  x ≥ 5

Since x is a natural number, this is the same as saying x > 4

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Explanation:

Let's solve for x

$x+12 < 4x-2\\\\12+2 < 4x-x\\\\14 < 3x\\\\3x > 14\\\\x > 14/3\\\\x > 4.667 \ \text{(approximate)}$

Since $x \in \mathbb{N}$, this means x is a natural number and a value from the set {1,2,3,4,...} aka the set of positive whole numbers. Zero is not in the set of natural numbers.

So we'll need to round that 4.667 to the nearest whole number to get x ≥ 5

If we were to replace x with anything from the set {5, 6, 7, 8, ...}, then that would make the original inequality to be true.

The notation x ≥ 5 and x > 4 are identical when x is a natural number, because we're describing the same solution set of any whole number 5 or larger.