Understanding Inequalities and Their Solutions

The video tutorial covers writing and solving one-step inequalities, focusing on the effects of addition, subtraction, multiplication, and division on inequalities. It explains how to graph inequalities and check solutions, and applies these concepts to solve real-world problems.

What happens to an inequality when you add the same number to both sides?

• The inequality symbol reverses.

• The inequality remains true.

• The inequality becomes an equation.

• The inequality becomes false.

When dividing both sides of an inequality by a negative number, what must you do to the inequality symbol?

• Keep it the same.

• Reverse it.

• Remove it.

• Change it to an equal sign.

In graphing inequalities, what does an open dot signify?

• The inequality is true.

• The inequality is false.

• The number is not included in the solution.

• The number is included in the solution.

In the context of inequalities, what does a closed dot on a graph indicate?

• The inequality is true.

• The number is included in the solution.

• The number is not included in the solution.

• The inequality is false.

How can you verify the solution of an inequality?

• By guessing a number.

• By graphing the inequality.

• By using a calculator.

• By substituting a number from the solution set.

If you multiply both sides of an inequality by a positive number, what happens to the inequality?

• The inequality becomes an equation.

• The inequality symbol reverses.

• It remains true.

• It becomes false.

How do you solve an inequality involving division by a negative number?

• Divide and keep the inequality symbol the same.

• Multiply instead of dividing.

• Divide and reverse the inequality symbol.

• Add the reciprocal of the number.

What must you remember when solving inequalities involving multiplication by a negative number?

• Keep the inequality symbol the same.

• Add instead of multiply.

• Reverse the inequality symbol.

• Subtract instead of multiply.

What is the first step in solving a real-world inequality problem?

• Check the solution with a calculator.

• Set up an inequality based on the problem.

• Guess the solution.

• Graph the solution.

In a real-world problem, if a submarine descends at a rate of 5 feet per second, how do you express this as an inequality?

• 5t > final elevation

• 5t < final elevation

• -5t > final elevation

• -5t < final elevation