To solve the inequality \(2x + 1 < \frac { 1} { 2} \):

1. Subtract 1 from both sides:
   \[2x + 1 - 1 < \frac { 1} { 2} - 1\]
   \[2x < \frac { 1} { 2} - 1\]
2. Simplify the right side:
   \[2x < \frac { 1} { 2} - \frac { 2} { 2} \]
   \[2x < - \frac { 1} { 2} \]
3. Divide both sides by 2:
   \[x < - \frac { 1} { 4} \]

Supplemental Knowledge

Inequalities are mathematical expressions that show the relationship between two values where one is not equal to the other. Solving inequalities involves finding the range of values that satisfy the inequality. Here are some key points to remember:

1. Basic Steps in Solving Inequalities:
   • Isolate the variable on one side of the inequality.
   • Perform similar operations as you would in an equation, but be mindful of reversing the inequality sign when multiplying or dividing by a negative number.
2. Graphical Representation:
   • Inequalities can be represented on a number line, showing all possible solutions.
   • Open circles indicate that a value is not included (e.g., \(x < 3\)), while closed circles indicate inclusion (e.g., \(x \leq 3\)).
3. Checking Solutions:
   • Always substitute back into the original inequality to verify if your solution is correct.

From Concepts to Reality

Consider budgeting a project where there is an upper spending limit of $5000; using inequalities like E  500 as your expenses to ensure staying under your spending cap and staying within budget, just as solving inequalities ensures finding valid solutions within given constraints. Solve these equations to stay within your spending limit!

Mastering algebraic concepts like inequalities is crucial for academic success and practical problem-solving. At UpStudy, we offer specialized tools such as our Algebra Inequalities Calculator to help you practice and understand these concepts better.
Visit UpStudy today to explore our extensive question bank and personalized learning tools that make mastering algebra both effective and enjoyable!