Find the solution set of the inequality two 𝑥 minus two is greater than four for all real values. Give your answer in interval notation.
The real numbers are all numbers that can be written as a decimal. These include rational and irrational numbers. Every real number corresponds to a point on the number line. In order to solve the inequality two 𝑥 minus two is greater than four, we will use the balancing method and our knowledge of inverse operations.
We begin by adding two to both sides. Four plus two is equal to six. Therefore, two 𝑥 is greater than six. We then divide both sides of this inequality by two. Two 𝑥 divided by two is 𝑥, and six divided by two is three. The solution to the inequality is 𝑥 is greater than three.
As we are asked for the solution set, we need to write this answer using set notation. 𝑥 can take any value between three and ∞. We use a curved bracket or parentheses next to the three as 𝑥 cannot be equal to three. If it could, we would use a square bracket. When dealing with ∞ or negative ∞, we always use a curved bracket as it can never reach either of these values. The solution set of the inequality is all real values between three and ∞.