Understanding Inequalities

The video tutorial explains how to form inequalities from verbal statements. It covers four main examples: the sum of a number and five being less than nine, the opposite of the difference of a number and seven being greater than or equal to three times the sum of the number and four, fifteen being greater than the opposite of five times the sum of a number and one, and eight minus a number being less than or equal to three times the number. Each example is broken down step-by-step, showing how to translate words into mathematical expressions and inequalities.

What is the inequality for the sum of a number and five being less than nine?

• n - 5 < 9

• n + 5 > 9

• n - 5 > 9

• n + 5 < 9

If n represents a number, what does the expression n + 5 represent?

• The product of a number and five

• The sum of a number and five

• The quotient of a number and five

• The difference of a number and five

What is the expression for the opposite of the difference of a number and seven?

• -(n - 7)

• n - 7

• 7 - n

• -(7 - n)

How is the expression 3 * (n + 4) interpreted?

• The sum of three and a number plus four

• Three times the sum of a number and four

• Three times the difference of a number and four

• The difference of three and a number plus four

What inequality represents fifteen being greater than the opposite of five times the sum of a number and one?

• 15 > -(5 * (n + 1))

• 15 < -(5 * (n + 1))

• 15 >= -(5 * (n + 1))

• 15 = -(5 * (n + 1))

What does the expression 5 * (n + 1) represent?

• Five times the difference of a number and one

• The difference of five and a number plus one

• The sum of five and a number plus one

• Five times the sum of a number and one

What is the inequality for eight minus a number being less than or equal to three times the number?

• 8 + n >= 3n

• 8 - n <= 3n

• 8 - n >= 3n

• 8 + n <= 3n

If n is a number, what does the expression 8 - n represent?

• The quotient of eight and a number

• The product of eight and a number

• The difference of eight and a number

• The sum of eight and a number

What does the expression 3n represent?

• Three divided by a number

• Three times a number

• Three minus a number

• Three plus a number

Which of the following is true for the inequality 8 - n <= 3n?

• n is less than or equal to 2

• n is greater than or equal to 2

• n is less than 2

• n is greater than 2