Find the solution set of three
𝑥 minus seven is less than negative four given that 𝑥 is a natural number.
Before trying to solve this
inequality, it is worth recalling what a natural number is. The natural numbers are the
nonnegative integers, for example, zero, one, two, three, four, and so on. We will now solve the
inequality given and find which of these numbers satisfy the inequality. Our inequality states that
three 𝑥 minus seven is less than negative four. We can solve this using inverse
operations. Our first step is to add seven
to both sides of the inequality, as the opposite of subtracting seven is adding
seven. Negative four plus seven is
equal to three, so three 𝑥 is less than three.
Our second and final step is to
divide both sides of this new inequality by three. Three 𝑥 divided by three is
equal to 𝑥, and three divided by three is equal to one. The solution to our inequality
is 𝑥 is less than one. This answer can be written in
interval notation, where 𝑥 can take any value less than one down to negative
∞. In this question, however,
we’re asked for the solution set. 𝑥 also needed to be a natural
number. The only natural number that is
less than one is zero. This means that the solution
set of the inequality three 𝑥 minus seven is less than negative four where 𝑥
is a natural number is the set containing the number zero.