Solving Inequalities and Boundary Points

The video tutorial covers solving inequalities efficiently. It begins with an introduction to inequalities and proceeds to solve and graph the inequalities 2x < 6 and -2x < 6. The tutorial explains how to test boundary points to determine the direction of solutions. An example problem, 3(10-2x) < 18, is solved step-by-step, demonstrating the process of solving the related equation, testing points, and graphing the solution. The video concludes with a summary of the goals, emphasizing the importance of solving inequalities and graphing solutions on a number line.

What is the first step in solving an inequality?

• Solving the related equation

• Drawing a number line

• Testing random values

• Graphing the solution

When solving 2x < 6, what value of x makes the inequality exactly equal to 6?

• x = 2

• x = 3

• x = 4

• x = 5

In the inequality 2x < 6, why is there an open circle at 3 on the number line?

• 3 is a solution

• 3 is less than 6

• 3 is not a solution

• 3 is greater than 6

For the inequality -2x < 6, which value of x is the boundary point?

• x = -3

• x = -4

• x = -2

• x = -1

In the inequality -2x < 6, which direction does the arrow point on the number line?

• Left of -3

• Right of -3

• Right of -2

• Left of -2

Why is it unnecessary to complete an entire table when solving inequalities?

• Tables are too complex

• Tables take too long to create

• Only one number needs to be tested

• Tables are not accurate

What should you do after finding the boundary point of an inequality?

• Test numbers on both sides of the boundary

• Graph the boundary point

• Draw a new number line

• Solve another equation

In the example 3(10 - 2x) < 18, what is the first step in solving the equation?

• Add 10 to both sides

• Subtract 10 from both sides

• Divide both sides by 3

• Multiply both sides by 3

After dividing both sides by 3 in the example 3(10 - 2x) < 18, what is the resulting equation?

• 10 - 2x = 3

• 10 - 2x = 6

• 10 - 2x = 0

• 10 - 2x = 18

What is the boundary point for the inequality 3(10 - 2x) < 18?

• x = 2

• x = 3

• x = 1

• x = 0