Multi-step linear inequalities

Sure! Here are the key points to learn when studying "Inequalities with variables on both sides":

1. Understanding Inequalities: Recognize the types of inequalities (e.g., <, >, ≤, ≥) and their meanings.

2. Isolate the Variable: Rearrange the inequality to get the variable on one side. This often involves adding/subtracting terms from both sides.

3. Combining Like Terms: Simplify both sides of the inequality by combining like terms.

4. Reversing the Inequality: If you multiply or divide by a negative number, remember to reverse the direction of the inequality.

5. Checking Your Solution: After solving the inequality, test a value from the solution set to ensure it satisfies the original inequality.

6. Graphing Solutions: Represent the solution on a number line to visualize the set of values that satisfy the inequality.

7. Compound Inequalities: Understand how to handle and solve compound inequalities, which involve more than one inequality.

These key points will help in effectively solving and understanding inequalities with variables on both sides.

When studying "Inequalities with variables on both sides (with parentheses)", focus on these key points:

1. Understand the Inequality Symbols: Familiarize yourself with the different inequality symbols (>, <, ≥, ≤) and their meanings.

2. Distribute and Simplify: If parentheses are present, use the distributive property to eliminate them by multiplying the terms inside by the factor outside.

3. Combine Like Terms: After distributing, combine like terms on both sides of the inequality to simplify the expression.

4. Isolate the Variable: Rearrange the inequality to isolate the variable on one side. This may involve adding, subtracting, multiplying, or dividing both sides.

5. Reverse the Inequality (if necessary): When multiplying or dividing both sides by a negative number, remember to reverse the direction of the inequality sign.

6. Check Your Solution: After finding the solution, check it by substituting values back into the original inequality to ensure it holds true.

7. Graphical Representation: Understand how to graph the solutions on a number line, indicating open or closed circles based on whether the inequality is strict or includes equality.

By mastering these points, you'll effectively handle inequalities with variables on both sides, even when parentheses are involved.

Sure! Here are the key points to learn when studying multi-step inequalities:

1. Understanding Inequalities: Recognize the symbols (>, <, ≥, ≤) and understand their meanings.

2. Combining Like Terms: Use properties of equality to combine like terms on both sides of the inequality.

3. Isolating the Variable: Just like in equations, manipulate the inequality to isolate the variable. This involves using addition, subtraction, multiplication, and division.

4. Reversing the Inequality: Remember to reverse the inequality sign when multiplying or dividing by a negative number.

5. Checking Solutions: Verify your solutions by substituting them back into the original inequality.

6. Graphing Solutions: Be able to represent solutions on a number line, using open or closed circles depending on whether the inequality is strict or inclusive.

7. Compound Inequalities: Understand how to solve and graph compound inequalities, which involve more than one inequality connected by "and" or "or."

By mastering these points, you'll develop a solid understanding of multi-step inequalities!