Understanding Compound Inequalities and Interval Notation

The video tutorial explains how to solve a compound inequality and express the solution using interval notation. It begins by identifying the two inequalities involved, solving each separately, and graphing them on a number line. The tutorial then combines the solutions to find the interval that satisfies both inequalities. Finally, it demonstrates how to express the solution using interval notation and as a compound inequality.

What does a compound inequality represent?

• An equation with no inequalities

• Two inequalities connected by 'and'

• Two inequalities connected by 'or'

• A single inequality

In the given compound inequality, what does the blue inequality represent?

• 3 - 4x is greater than or equal to -13

• 3 - 4x is less than -13

• 3 - 4x is greater than -13

• 3 - 4x is equal to -13

What is the first step in solving the inequality 3 - 4x > -16?

• Divide both sides by 4

• Multiply both sides by 4

• Subtract 3 from both sides

• Add 3 to both sides

When dividing both sides of an inequality by a negative number, what must you remember to do?

• Add the same number to both sides

• Keep the inequality symbol the same

• Subtract the same number from both sides

• Reverse the inequality symbol

What is the solution to the inequality 3 - 4x ≤ 1?

• x ≤ 1/2

• x ≥ 1/2

• x > 1/2

• x < 1/2

How is the solution to the inequality x ≥ 1/2 represented on the number line?

• Closed point at 1/2 with an arrow to the right

• Open point at 1/2 with an arrow to the right

• Closed point at 1/2 with an arrow to the left

• Open point at 1/2 with an arrow to the left

What does the interval notation [1/2, 4) represent?

• All numbers greater than 1/2 and less than 4

• All numbers less than 1/2 and greater than 4

• All numbers greater than or equal to 1/2 and less than 4

• All numbers greater than 1/2 and less than or equal to 4

Which of the following is true about the interval [1/2, 4)?

• It includes both 1/2 and 4

• It includes 1/2 but not 4

• It includes neither 1/2 nor 4

• It includes 4 but not 1/2

How can the solution to the compound inequality be expressed?

• As a single inequality

• As a graph only

• As a compound inequality, graph, and interval notation

• As a graph and interval notation only

What is the equivalent expression for the solution x < 4 and x ≥ 1/2?

• x is equal to 1/2 and 4

• x is greater than 1/2 or less than 4

• x is less than 1/2 or greater than 4

• x is between 1/2 and 4