Solving One-Variable Inequalities

The video tutorial covers solving inequalities in one variable, emphasizing the similarities to solving equations but with the addition of inequality symbols. It explains the process of solving inequalities, including distributing, adding, and dividing, and highlights the importance of flipping the inequality sign when multiplying or dividing by a negative number. The tutorial also demonstrates how to graph solutions on a number line, using open circles and shading to represent possible solutions. Several examples are provided to illustrate the concepts, including cases with no solutions and infinitely many solutions.

What does the line underneath the inequality symbol indicate?

• It means the values are not equal.

• It means the values are greater than.

• It means the values can be equal.

• It means the values are less than.

When solving an inequality, what must you do if you multiply or divide by a negative number?

• Keep the inequality sign the same.

• Flip the inequality sign.

• Subtract the same number from both sides.

• Add the same number to both sides.

What is the first step in solving the inequality -3(2x + 2) < 10?

• Subtract 6 from both sides.

• Divide by -3.

• Distribute the -3.

• Add 6 to both sides.

How do you represent the solution x > -8/3 on a number line?

• With a closed circle at -8/3 and shading to the left.

• With an open circle at -8/3 and shading to the right.

• With a closed circle at -8/3 and shading to the right.

• With an open circle at -8/3 and shading to the left.

What does an open circle on a number line represent?

• The value is greater than the solution set.

• The value is less than the solution set.

• The value is not included in the solution set.

• The value is included in the solution set.

In the inequality 2(4 - 2x) > 1, what is the result after distributing the 2?

• 4 - 2x > 1

• 4 + 2x > 1

• 8 + 4x > 1

• 8 - 4x > 1

When graphing the solution x < 7/4, where would you place the open circle?

• At 2

• Between 1 and 2

• Between 0 and 1

• At 1

What does it mean if the inequality statement is false after solving?

• There is no solution.

• The solution is negative.

• There are infinitely many solutions.

• The solution is zero.

If the inequality statement is true after solving, what does it indicate?

• There are infinitely many solutions.

• The solution is positive.

• There is one solution.

• There is no solution.

How can you determine if an inequality statement is true or false?

• By adding the same number to both sides.

• By solving the inequality and checking the values.

• By ignoring the inequality sign.

• By guessing the values.