Solving and Graphing One-Variable Inequalities

This video tutorial introduces solving inequalities involving one variable. It covers the basics of inequalities, how to graph them on a number line, and the differences between solving equations and inequalities. The tutorial provides examples of simple inequalities and explains the importance of flipping the inequality sign when multiplying or dividing by a negative number. It concludes with more complex examples to ensure comprehensive understanding.

What is the main difference between solving equations and solving inequalities?

• You cannot graph inequalities.

• Inequalities involve a range of solutions instead of a single solution.

• You use different mathematical operations for inequalities.

• The variable is always on the left side in inequalities.

How do you represent the inequality x > 3 on a number line?

• A closed circle at 3 and shading to the right.

• An open circle at 3 and shading to the right.

• A closed circle at 3 and shading to the left.

• An open circle at 3 and shading to the left.

What does a closed circle on a number line indicate?

• The number is not included in the solution.

• The inequality is greater than.

• The number is included in the solution.

• The inequality is less than.

If x - 7 > -5, what is the solution for x?

• x > 2

• x < -2

• x < 2

• x > -2

How do you graph the solution of 2t < 6 on a number line?

• Open circle at 3 and shading to the right.

• Closed circle at 3 and shading to the right.

• Closed circle at 3 and shading to the left.

• Open circle at 3 and shading to the left.

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

• Keep the inequality sign the same.

• Subtract the same number from both sides.

• Flip the direction of the inequality sign.

• Add the same number to both sides.

What is the solution for the inequality -5x < 10?

• x > -2

• x < -2

• x > 2

• x < 2

How do you solve the inequality 3x - 1 ≥ -4?

• x ≥ -1

• x ≤ -1

• x ≤ 1

• x ≥ 1

What is the solution for the inequality y ≤ 7y - 24?

• y ≤ -4

• y ≥ 4

• y ≥ -4

• y ≤ 4

How do you solve the inequality 2 - x < 4 + x?

• x < -1

• x > 1

• x > -1

• x < 1