Exploring Compound Inequalities in Algebra

The video tutorial covers compound inequalities, explaining how they involve multiple constraints. It demonstrates solving compound inequalities through examples, including both 'and' and 'or' scenarios. The tutorial illustrates how to express solutions in interval notation and graph them on a number line. It also highlights the importance of understanding the difference between 'and' and 'or' inequalities in determining solution sets.

What is a compound inequality?

• An inequality with only one constraint

• An inequality with more than one constraint

• An equation with no constraints

• An equation with only one solution

How can the compound inequality -5 ≤ x - 4 ≤ 13 be rewritten?

• -5 = x - 4 and x - 4 = 13

• -5 ≥ x - 4 and x - 4 ≥ 13

• -5 ≤ x - 4 and x - 4 ≤ 13

• -5 < x - 4 and x - 4 < 13

What is the solution set for the inequality -5 ≤ x - 4?

• x < -1

• x > -1

• x ≥ -1

• x ≤ -1

How is the solution set for x represented on a number line for -1 ≤ x ≤ 17?

• A closed circle at -1 and an open circle at 17 with shading in between

• An open circle at -1 and 17 with shading in between

• A closed circle at -1 and 17 with shading in between

• An open circle at -1 and a closed circle at 17 with shading in between

What happens to the inequality sign when you divide both sides by a negative number?

• It becomes an equal sign

• It swaps around

• It remains the same

• It disappears

What is the solution set for the inequality 2 - 5x ≤ 7?

• x ≥ -1

• x ≤ -1

• x > -1

• x < -1

How is the solution set for x represented on a number line for -1 ≤ x < 2 and 4/5?

• A closed circle at -1 and an open circle at 2 and 4/5 with shading in between

• An open circle at -1 and 2 and 4/5 with shading in between

• An open circle at -1 and a closed circle at 2 and 4/5 with shading in between

• A closed circle at -1 and 2 and 4/5 with shading in between

What does 'or' mean in compound inequalities?

• Neither condition must be satisfied

• The conditions are ignored

• Only one of the conditions must be satisfied

• Both conditions must be satisfied

What is the solution set for the inequality 4x - 1 ≥ 7?

• x < 2

• x ≥ 2

• x ≤ 2

• x > 2

What is the solution set for the inequality 9x/2 < 3?

• x ≤ 2/3

• x > 2/3

• x ≥ 2/3

• x < 2/3