Understanding and Solving Inequalities

The video tutorial covers solving and graphing inequalities, starting with an introduction to the concept and the use of boundary points on a number line. It explains how to solve inequalities similarly to equations, emphasizing the importance of switching the inequality sign when multiplying or dividing by a negative number. The tutorial includes graphing solutions and provides practice problems to reinforce the concepts.

What symbol is used to represent 'less than or equal to' in inequalities?

• <

• ≥

• >

• ≤

When graphing inequalities, what does a filled-in boundary point indicate?

• The number is a midpoint.

• The number is irrelevant.

• The number is included in the solution.

• The number is excluded from the solution.

How do you solve an inequality to isolate the variable?

• Subtract the same number from both sides.

• Ignore the variable.

• Add the same number to both sides.

• Perform the same operation on both sides.

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Keep the inequality sign the same.

• Switch the direction of the inequality sign.

• Subtract a positive number from both sides.

• Add a positive number to both sides.

In the inequality x > -3, what does the boundary point at -3 represent?

• x is not equal to -3.

• x is greater than -3.

• x is less than -3.

• x is equal to -3.

What is the first step in solving an inequality with a fraction?

• Ignore the fraction.

• Divide by the fraction.

• Multiply through by the least common denominator.

• Add the fraction to both sides.

When solving the inequality 5x < 20, what is the solution for x?

• x < 4

• x ≤ 4

• x > 4

• x = 4

If you have the inequality -2x > 6, what is the correct solution for x?

• x < 3

• x > 3

• x > -3

• x < -3

What is the boundary point for the inequality x ≤ 5?

• 5, and it is open

• 5, and it is filled

• 4, and it is open

• 6, and it is filled

In the inequality 3x ≥ 9, what is the solution for x?

• x ≤ 3

• x ≥ 3

• x < 3

• x > 3