Properties of Inequalities

This video introduces inequalities, explaining that they are statements where one expression is greater or less than another. It covers three main properties: the addition property, where adding the same number to both sides maintains the inequality; the multiplication property with positive numbers, where multiplying both sides by a positive number maintains the inequality; and the multiplication property with negative numbers, where multiplying both sides by a negative number reverses the inequality. The video also generalizes these properties to include greater than or equal to and less than or equal to scenarios, emphasizing caution when dealing with negative numbers.

What is an inequality?

• A statement that one expression is the square of another.

• A statement that two expressions are equal.

• A statement that one expression is greater than or less than another.

• A statement that two expressions are not equal.

If a < b, what happens when you add the same number to both sides?

• The inequality becomes invalid.

• The inequality becomes an equality.

• The inequality reverses.

• The inequality remains the same.

Which of the following is an example of the first property of inequalities?

• 5 + 3 >= 7 + 3

• 5 + 3 < 7 + 3

• 5 + 3 = 7 + 3

• 5 + 3 > 7 + 3

What is the effect of adding the same number to both sides of an inequality?

• The inequality becomes invalid.

• The inequality reverses.

• The inequality remains the same.

• The inequality becomes an equality.

What does the second property of inequalities state?

• If a < b and c is negative, then ac > bc.

• If a < b and c is positive, then ac < bc.

• If a < b and c is negative, then ac < bc.

• If a < b and c is positive, then ac > bc.

If 5 < 7, what is true about 5 * 3 and 7 * 3?

• 5 * 3 > 7 * 3

• 5 * 3 = 7 * 3

• 5 * 3 < 7 * 3

• 5 * 3 <= 7 * 3

Which statement is true about multiplying inequalities by a positive number?

• The inequality becomes invalid.

• The inequality reverses.

• The inequality remains the same.

• The inequality becomes an equality.

What happens to an inequality when both sides are multiplied by a negative number?

• The inequality remains the same.

• The inequality becomes invalid.

• The inequality becomes an equality.

• The inequality reverses.

If a < b and c is negative, what is true about ac and bc?

• ac >= bc

• ac = bc

• ac < bc

• ac > bc

Which of the following is an example of the third property of inequalities?

• 5 * -2 > 7 * -2

• 5 * -2 = 7 * -2

• 5 * -2 >= 7 * -2

• 5 * -2 < 7 * -2