Solving Inequalities in Algebra

The video tutorial explains the difference between equations and inequalities, focusing on solving inequalities. It covers solving one-step inequalities, the importance of reversing the inequality sign when multiplying or dividing by negative numbers, and provides a practical example involving weight limits. The tutorial also demonstrates how to graph solutions of inequalities, highlighting the differences between strict and non-strict inequalities.

What is an inequality?

• A mathematical sentence with a less than, less than or equal to, greater than, or greater than or equal to sign.

• A mathematical sentence that does not involve variables.

• A mathematical sentence that can only have one solution.

• A mathematical sentence with an equal sign.

How do you solve a one-step inequality?

• By graphing the inequality on a number line.

• By checking every possible solution.

• By adding or subtracting the same number from both sides.

• By multiplying or dividing both sides by the variable.

Why can't every number in the solution set of an inequality be checked?

• Because inequalities do not have solution sets.

• Because only whole numbers can be solutions.

• Because it's not necessary as long as one solution works.

• Because the solution set is infinite.

What happens to the inequality sign when you add or subtract the same number from both sides?

• It reverses.

• It remains unchanged.

• It disappears.

• It becomes an equal sign.

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Nothing special is required.

• Subtract 1 from both sides.

• Add 1 to both sides.

• Reverse the inequality sign.

In the elevator scenario, what is the maximum number of boxes that can be safely transported?

• 32 boxes

• 32.5 boxes

• 33 boxes

• 31 boxes

How is a solution to an inequality represented on a graph when the inequality is 'greater than or equal to'?

• With an open circle on the number and a line extending to the left.

• With a closed circle on the number and a line extending to the right.

• With an open circle on the number and a line extending to the right.

• With a closed circle on the number and a line extending to the left.

What is the correct graph representation for an inequality with a 'less than' condition?

• An open circle with a line extending to the left.

• An open circle with a line extending to the right.

• A closed circle with a line extending to the right.

• A closed circle with a line extending to the left.

What is the purpose of graphing solutions of inequalities?

• To prove that inequalities have no solution.

• To visually represent the range of possible solutions.

• To convert the inequality into an equation.

• To find the exact numerical solution.

What does an open circle on a graph indicate about the solution to an inequality?

• The solution set includes all numbers.

• The solution set is empty.

• The number is not included in the solution set.

• The number is included in the solution set.