Solving One-Variable Inequalities and Graphing on a Number Line

The video tutorial covers solving inequalities, starting with simple examples and progressing to more complex cases. It explains how to isolate variables, handle negative coefficients, and solve inequalities with variables on both sides. Special cases, such as no solution scenarios, are also discussed. The tutorial emphasizes the importance of flipping the inequality sign when multiplying or dividing by a negative number.

What is the first step in solving the inequality -4 + 5x < 16?

• Subtract 4 from both sides

• Add 4 to both sides

• Multiply both sides by 5

• Divide both sides by 5

When solving inequalities, what happens if you divide both sides by a negative number?

• The inequality sign stays the same

• The inequality sign changes direction

• The inequality sign is removed

• The inequality sign becomes an equal sign

In the inequality -2x ≥ 10, what is the result after dividing both sides by -2?

• x ≤ 5

• x ≥ -5

• x ≥ 5

• x ≤ -5

How do you handle fractions when solving inequalities?

• Subtract the fractions from both sides

• Multiply everything by the denominator to clear the fractions

• Add the fractions to both sides

• Divide everything by the numerator to clear the fractions

What is the result of solving the inequality 8 > -x + 7?

• x > 1

• x < 1

• x < -1

• x > -1

When solving 2x - 6 < 3x + 3, what is the first step?

• Subtract 3x from both sides

• Subtract 6 from both sides

• Add 6 to both sides

• Add 3x to both sides

What is the final solution to the inequality 2x - 6 < 3x + 3?

• x ≥ 9

• x ≤ -9

• x ≥ -9

• x ≤ 9

What does it mean if the variable cancels out on both sides of an inequality?

• There is no solution

• There is one solution

• There are infinite solutions

• The inequality sign changes direction

If 1 < -1 is the result after solving an inequality, what does it imply?

• There are infinite solutions

• There is one solution

• There is no solution

• The inequality sign changes direction

If the result of an inequality is always true, what does it imply?

• The inequality sign changes direction

• There are infinite solutions

• There is one solution

• There is no solution