Inequalities, Absolute Values, and Factoring

The video covers practice problems from unit seven, lesson eight. It begins with a discussion on book prices at a sale, using inequalities to determine the maximum price. Next, it analyzes the time Karen spent on homework, using reasoning to evaluate different time scenarios. The video then calculates the volume of a rectangular prism with varying dimensions. It continues by matching mathematical statements with their English descriptions, focusing on absolute values and comparisons. Finally, it demonstrates the use of the distributive property to simplify algebraic expressions.

What is the maximum price a book could be at the sale if all books cost less than five dollars?

• $4.50

• $5.00

• $4.99

• $5.01

Which inequality represents the cost of books at the sale?

• P ≥ 5

• P < 5

• P ≤ 5

• P > 5

If Karen started her homework before 7 and finished after 8, which statement is definitely true?

• She worked more than 1 hour

• She worked exactly 1 hour

• She worked less than 2 hours

• She worked less than 1 hour

What is the expression for the volume of a rectangular prism with length 4 and width and height D?

• D^3

• 4D^2

• 4D^3

• 4D

Calculate the volume of the prism when D is 2.

• 2

• 16

• 4

• 8

Which statement is true about the absolute values of -15 and -12?

• |-15| = 12

• |-15| > |-12|

• |-15| = |-12|

• |-15| < |-12|

What is the English equivalent of the statement: 12 is greater than -12?

• 12 > -12

• 12 = -12

• 12 ≤ -12

• 12 < -12

How can you express 2a + 7a using the distributive property?

• 9a

• 7(2a)

• 2(a + 7)

• a(2 + 7)

Which of the following is a correct factorization of 5z - 10?

• z(5 - 10)

• 5z(1 - 2)

• 5(z - 2)

• 10(z - 5)

What is the result of factoring 2x - 1/2 using the distributive property?

• 2(x - 1/4)

• 1/2(4x - 1)

• 2x(1 - 1/2)

• x(2 - 1/2)