Solving Inequalities and Their Properties

The video tutorial covers solving two-step inequalities, graphing them on a number line, and the special rule of reversing inequality signs when multiplying or dividing by negative numbers. The lesson includes examples and practice problems to reinforce the concepts, with a focus on using the SAD MAP method for solving inequalities.

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

• Divide both sides by a constant

• Add a constant to both sides

• Subtract a constant from both sides

• Multiply both sides by a constant

When graphing an inequality, what does an open circle on the number line represent?

• The number is included in the solution

• The number is not included in the solution

• The inequality is less than or equal to

• The inequality is greater than or equal to

What must you remember to do when multiplying or dividing both sides of an inequality by a negative number?

• Keep the inequality sign the same

• Subtract a constant from both sides

• Add a constant to both sides

• Flip the inequality sign

In the inequality 6 - x > 3, what is the first step to isolate x?

• Divide both sides by 6

• Multiply both sides by -1

• Subtract 6 from both sides

• Add 6 to both sides

What is the solution to the inequality 3x + 4 < 16?

• x > 12

• x < 12

• x > 4

• x < 4

What is the result of dividing both sides of the inequality -2m ≤ 30 by -2?

• m ≥ -15

• m ≥ 15

• m ≤ 15

• m ≤ -15

Which property might be used when solving inequalities with variables on both sides?

• Identity property

• Associative property

• Commutative property

• Distributive property

What is a common strategy to avoid dealing with negative coefficients in inequalities?

• Pick on the smaller variable

• Pick on the larger variable

• Always add to both sides

• Always subtract from both sides

What happens to the inequality sign when you multiply both sides by a positive number?

• It remains the same

• It disappears

• It flips direction

• It becomes an equal sign

What is the key difference between solving equations and inequalities?

• Equations have equal signs

• Inequalities have graphs

• Inequalities have equal signs

• Equations have variables