Writing and Graphing Inequalities on a Number Line

This video tutorial covers the basics of writing and graphing inequalities. It explains the symbols used in inequalities, how to determine solution sets, and how to graph these on a number line. The tutorial also provides guidance on converting sentences into inequalities and checking if a value is a solution. Key phrases associated with inequality symbols are discussed, and exercises are provided to practice these concepts.

What is an inequality in mathematics?

• A sentence that shows the equality of two expressions.

• A sentence that only uses multiplication and division.

• A sentence that compares expressions using symbols like <, >, ≤, or ≥.

• A sentence that only uses addition and subtraction.

Which symbol represents 'greater than'?

• ≤

• ≥

• >

• <

How is the solution set of x < 2 represented on a number line?

• A closed circle at 2 with shading to the left.

• An open circle at 2 with shading to the left.

• A closed circle at 2 with shading to the right.

• An open circle at 2 with shading to the right.

What does a closed circle on a number line indicate?

• The number is not part of the solution set.

• The inequality is strict.

• The inequality is not strict.

• The number is part of the solution set.

Which phrase can be used for the symbol '≤'?

• Is at least

• Is at most

• Is fewer than

• Is more than

How would you write '12 is greater than or equal to 5 times a number n' as an inequality?

• 12 < 5n

• 12 ≤ 5n

• 12 ≥ 5n

• 12 > 5n

What does the word 'difference' indicate in an inequality?

• Multiplication

• Subtraction

• Addition

• Division

If 19 is substituted for d in the inequality d - 7 < 12, is 19 a solution?

• Yes, because 19 - 7 is greater than 12.

• No, because 19 - 7 is equal to 12.

• Yes, because 19 - 7 is less than 12.

• No, because 19 - 7 is not equal to 12.

How would you graph the inequality x > -1 on a number line?

• An open circle at -1 with shading to the left.

• A closed circle at -1 with shading to the left.

• An open circle at -1 with shading to the right.

• A closed circle at -1 with shading to the right.

What inequality represents a graph with an open circle at 0 and shading to the left?

• x ≤ 0

• x < 0

• x ≥ 0

• x > 0