Determine the solution set of nine 𝑥 plus five is greater than or equal to negative four given that 𝑥 is an integer.
The integer values are all positive and negative whole numbers. In order to solve our inequality, we will use the balancing method and our knowledge of inverse operations. The solution set will be all integers that satisfy this.
We begin by subtracting five from both sides of the inequality. Negative four minus five is equal to negative nine. Therefore, nine 𝑥 is greater than or equal to negative nine. We then divide both sides by nine. Nine 𝑥 divided by nine is equal to 𝑥, and negative nine divided by nine is negative one. Therefore, 𝑥 is greater than or equal to negative one.
As we want the solution set, we need to write our answer using set notation. 𝑥 could be any of the following integers: negative one, zero, one, two, and so on. Any whole number greater than or equal to negative one would satisfy the inequality.