What is an inequality?

What is the rule for multiplying or dividing both sides of an inequality by a negative number?

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. For example, if -2x < 6, then x > -3. Hint: Always remember to flip the inequality sign when dealing with negative numbers.

What is a tip for solving compound inequalities?

When solving compound inequalities, treat each part separately and then find the intersection of the two solution sets. Hint: Focus on breaking down the compound inequality into smaller, manageable pieces.

Solve the inequality: 3x - 4 ≥ 2x + 5.

Subtract 2x from both sides: x - 4 ≥ 5. Then add 4 to both sides: x ≥ 9. Hint: Start by isolating the variable on one side of the inequality.

Solve the inequality: -2(x + 3) < 8.

Distribute -2: -2x - 6 < 8. Add 6 to both sides: -2x < 14. Divide by -2 and reverse the inequality: x > -7. Hint: Don’t forget to reverse the inequality when dividing by a negative number.

What is the solution set for the inequality: x + 4 < 2 or 3x - 5 ≥ 4?

First, solve x + 4 < 2: x < -2. Then solve 3x - 5 ≥ 4: 3x ≥ 9, so x ≥ 3. The solution set is x < -2 or x ≥ 3. Hint: Pay attention to the 'or' in the compound inequality.

What is a key property of inequalities involving absolute values?

For an inequality involving an absolute value, |x| < a means -a < x < a, while |x| ≥ a means x ≤ -a or x ≥ a. Hint: Remember to consider both the positive and negative cases for absolute values.

If 5x - 3 > 2x + 6, what is the value of x?

Subtract 2x from both sides: 3x - 3 > 6. Then add 3 to both sides: 3x > 9. Finally, divide by 3: x > 3. Hint: Isolate the variable step by step.