Solving Algebraic Inequalities

The video tutorial introduces inequalities, explaining their difference from equations. It covers solving simple inequalities, using symbols, and representing solutions on a number line. The tutorial highlights the special rule of reversing inequality symbols when multiplying or dividing by negative numbers, providing examples and rationalizations for this rule.

What is the primary difference between an equation and an inequality?

• An equation involves variables, while an inequality does not.

• An equation is always true, while an inequality is always false.

• An equation shows equality, while an inequality shows inequality.

• An equation can only have one solution, while an inequality cannot.

Which of the following values is a solution for the inequality x > 3?

• 0

• 3.5

• 3

• 2

How is the solution to x > 3 represented on a number line?

• With a closed circle at 4

• With a closed circle at 3

• With an open circle at 4

• With an open circle at 3

What does the symbol '≥' mean in an inequality?

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

If 3x + 4 ≥ 16, what is the solution for x?

• x > 4

• x < 4

• x ≥ 4

• x ≤ 4

What must be done to the inequality symbol when multiplying or dividing both sides by a negative number?

• Remove it entirely

• Leave it unchanged

• Reverse its direction

• Change it to an equal sign

Why does multiplying or dividing by a negative number require flipping the inequality symbol?

• Because it changes the values to positive

• Because it simplifies the inequality

• Because it inverts the number line

• Because it makes the inequality false