Determine the solution set of two minus 𝑥 is less than or equal to negative eight, where 𝑥 is contained in the set of positive integers.
The first thing we can do is say two minus 𝑥 is less than or equal to negative eight. We can solve this inequality for 𝑥 by first subtracting two from both sides of the equation, which tells us that negative 𝑥 is less than or equal to negative 10. And from there, we want to multiply the entire inequality by negative one. And that means we’ll be flipping the sign. When we multiply inequalities by negative one, we change the direction of the sign. Negative 𝑥 becomes positive 𝑥 and negative 10 becomes positive 10.
We know that 𝑥 can only be positive integers, and so we wanna write this using set notation, which will look like this. 𝑥 is equal to open brackets 10, 11, 12, continuing closed brackets, all the values of positive integers that are 10 or greater.