Solving Inequalities and Their Graphs

This video tutorial covers solving multi-step inequalities, including simplifying each side, using inverse operations, and graphing solutions. It provides examples of solving inequalities with variables on both sides, cases with no solution, and all real numbers. Additionally, it includes a word problem involving calculating a mean score to advance in a game.

What is the first step in solving a multi-step inequality?

• Simplify each side of the inequality

• Isolate the variable

• Multiply by a negative number

• Graph the solution

When solving an inequality, when should you flip the inequality sign?

• When subtracting a constant

• When multiplying or dividing by a negative number

• When graphing the solution

• When adding a constant

In the inequality y/(-6) + 7 < 9, what is the first operation to perform?

• Subtract 7 from both sides

• Multiply by -6

• Add 7 to both sides

• Divide by -6

How do you graph the solution y > -12 on a number line?

• Open circle at -12, arrow pointing left

• Closed circle at -12, arrow pointing right

• Open circle at -12, arrow pointing right

• Closed circle at -12, arrow pointing left

What is the result of solving the inequality 6x - 5 < 2x + 11?

• x ≤ 4

• x = 4

• x > 4

• x < 4

What does it mean if an inequality simplifies to a false statement like -3 > 12?

• The inequality needs to be re-evaluated

• The inequality is incorrect

• The inequality has all real numbers as solutions

• The inequality has no solution

What does it mean if an inequality simplifies to a true statement like -2 ≤ 7?

• The inequality has no solution

• The inequality has all real numbers as solutions

• The inequality needs to be re-evaluated

• The inequality is incorrect

In a real-life problem, if you need an average score of at least 90, what inequality represents the score needed in the fifth game?

• x < 98

• x > 98

• x ≤ 98

• x ≥ 98

What is the mean score if the scores are 95, 91, 77, 89, and x, and the mean needs to be at least 90?

• x > 90

• x < 90

• x = 90

• x ≥ 90

What is the correct approach to solve for x in the inequality 352 + x/5 ≥ 90?

• Add 352 to both sides

• Multiply both sides by 5

• Divide both sides by 5

• Subtract 352 from both sides