Solving Multistep Inequalities Challenge

The video tutorial covers solving multi-step inequalities, starting with an introduction to the topic and progressing through examples that demonstrate solving inequalities with variables on both sides. It highlights the importance of using inverse operations and graphing solutions on a number line. Special cases, such as no solution and infinite solutions, are discussed. The tutorial concludes with a summary and mentions real-world applications of inequalities.

What is the first step in solving the inequality y/(-6) < 2?

• Multiply both sides by -6

• Subtract 7 from both sides

• Add 7 to both sides

• Divide both sides by -6

When multiplying or dividing by a negative number in an inequality, what must you remember to do?

• Keep the inequality sign the same

• Flip the inequality sign

• Subtract the same number from both sides

• Add the same number to both sides

In the inequality y > -12, how should the number line be graphed?

• Closed circle at -12, shade to the right

• Open circle at -12, shade to the right

• Open circle at -12, shade to the left

• Closed circle at -12, shade to the left

What is the solution to the inequality 2x ≥ 12?

• x < 6

• x ≤ 6

• x > 6

• x ≥ 6

How should the number line be graphed for the inequality x ≥ 6?

• Closed circle at 6, shade to the right

• Closed circle at 6, shade to the left

• Open circle at 6, shade to the left

• Open circle at 6, shade to the right

What is the solution to the inequality 4x - 5 < 11?

• x ≥ 4

• x < 4

• x > 4

• x ≤ 4

In the inequality 4x - 5 < 11, where should the open circle be placed on the number line?

• At 4

• At -4

• At -5

• At 0

What is the result when both sides of the inequality 8x - 3 > 8x + 12 are simplified?

• -3 > 12

• 8x > 8x

• 0 > 15

• 0 < 15

What does it mean when an inequality results in a false statement like -3 > 12?

• The solution is x < 0

• The solution is x > 0

• There is no solution

• There are infinitely many solutions

What does it mean when an inequality results in a true statement like -2 ≤ 7?

• The solution is x = 0

• There are infinitely many solutions

• There is one solution

• There are no solutions