Solving Rational Number Inequalities

The video tutorial explains how to solve inequalities using addition and subtraction, emphasizing the importance of inverse operations and maintaining balance by applying the same operation to both sides. It provides examples of solving inequalities and graphing the solutions, demonstrating the process step-by-step. The tutorial covers key concepts such as isolating the variable, using inverse operations, and graphing solutions on a number line.

What is the 'Golden Rule' when solving inequalities?

• Perform the same operation on both sides of the inequality

• Subtract the same value from both sides only

• Only add to both sides, never subtract

• Always switch the inequality sign when adding or subtracting

What happens to the inequality if we add the same number to both sides?

• It becomes impossible to solve

• The inequality reverses

• The inequality remains true

• The inequality becomes an equation

How do you solve an inequality with a negative number on one side?

• By adding a positive number to both sides

• By dividing both sides by the negative number

• By subtracting a positive number from both sides

• By multiplying both sides by -1

In the example, what operation is performed to isolate 'W'?

• Addition

• Division

• Subtraction

• Multiplication

What is the result of 'W' in the addition example?

• W < -0.8

• W > -0.8

• W = -0.8

• W <= -0.8

How is the solution graphed for 'W <= -0.8'?

• Closed circle at -0.8 with arrow to the right

• Open circle at -0.8 with arrow to the left

• Closed circle at -0.8 with arrow to the left

• Open circle at -0.8 with arrow to the right

What operation is used to isolate 'X' in the subtraction example?

• Addition of three-fourths

• Subtraction of three-fourths

• Multiplication by three-fourths

• Division by three-fourths

What is the final inequality for 'X' in the subtraction example?

• X > 3.75

• X >= 3.75

• X < 3.75

• X <= 3.75

How is 'X > 3.75' graphed?

• Closed circle at 3.75 with arrow to the left

• Open circle at 3.75 with arrow to the right

• Closed circle at 3.75 with arrow to the right

• Open circle at 3.75 with arrow to the left

What is the best practice when graphing inequalities?

• Use an open circle when the variable is not included in the solution

• Use a closed circle when the variable equals the number

• Always use a closed circle

• Graph only on the positive side of the number line