Solve each inequality. Give the solution set using interval notation. 11x≥2(x-4)

Key Concepts

Inequalities

Inequalities are mathematical statements that express the relationship between two expressions that are not necessarily equal. They use symbols such as '≥' (greater than or equal to), '≤' (less than or equal to), '>' (greater than), and '<' (less than). Understanding how to manipulate and solve inequalities is crucial for finding solution sets.

Solving Inequalities

Solving inequalities involves isolating the variable on one side of the inequality sign. This process often includes performing operations such as addition, subtraction, multiplication, or division, while being mindful that multiplying or dividing by a negative number reverses the inequality sign. The goal is to express the solution in a clear and concise manner.

Interval Notation

Interval notation is a way of representing the solution set of an inequality using intervals. It uses parentheses '()' to indicate that an endpoint is not included and brackets '[]' to indicate that an endpoint is included. For example, the interval [a, b) includes 'a' but not 'b', which is essential for clearly communicating the range of values that satisfy the inequality.