solving compound inequality can someone please help I don't understand.
http://www.sparknotes.com/math/algebra1/compoundinequalities/section4.rhtml
http://www.khanacademy.org/math/algebra/ck12-algebra-1/v/compound-inequalities
Certainly! I can help you understand how to solve compound inequalities.
A compound inequality is an inequality that contains more than one mathematical expression connected by the words "and" or "or". The goal is to find the values that satisfy both or either of the expressions.
Here's a step-by-step approach to solving compound inequalities:
1. Identify the type of compound inequality:
- If the inequality is connected by "and" (e.g., x > 2 and x < 5), it means the solution must satisfy both inequalities. In this case, we are looking for the overlap between the two inequalities.
- If the inequality is connected by "or" (e.g., x > 2 or x < 5), it means the solution can satisfy either of the inequalities. In this case, we are looking for the union of the two inequalities.
2. Solve each inequality separately:
- Treat each inequality as if it were a standalone inequality and solve for the variable.
- Remember to reverse the inequality sign when multiplying or dividing by a negative number.
3. Graph each solution on a number line:
- Mark the solutions for each inequality on a number line.
- Use an open circle for > or <, and a closed circle for ≥ or ≤.
4. Combine the solutions based on the type of compound inequality:
- For "and" compound inequalities, shade the overlapping region between the two solutions.
- For "or" compound inequalities, shade the combined region of the two solutions.
5. Write the final solution in interval notation:
- Express the solution using interval notation, which represents the range of values on the number line.
It's important to remember that compound inequalities follow the same rules as simple inequalities, such as adding or subtracting the same value to both sides, multiplying or dividing by the same positive value, and reversing the inequality sign when multiplying or dividing by a negative value.
I hope this explanation helps you understand how to solve compound inequalities!