Combining Like Terms: Practice and Review

This video tutorial covers several problems related to combining like terms, evaluating expressions, and understanding inequalities. It begins with an introduction to the concept of equivalence in expressions, followed by a detailed analysis of expressions that can be subtracted to achieve a specific result. The tutorial then explores statements that hold true for any value of x, and describes situations using inequalities. Finally, it addresses a practical problem involving the rate of water flow into a bucket, emphasizing the importance of understanding rates and volumes.

Andre claims that 10x + 6 and 5x + 11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?

• No, because they are never equivalent.

• No, because they are not equivalent when x is 0.

• Yes, because they are always equivalent.

• Yes, because they are equivalent when x is 0.

Which expression can be subtracted from 9x to result in 3x + 5?

• 6x - 5

• 5x + 6

• 6x - 11

• 6x + 5

What is the result of combining like terms in the expression 9x - 6x + 5?

• 3x + 5

• 3x - 5

• 9x + 5

• 15x - 5

Which of the following statements is true for any value of x?

• 7x + 2x - 1 = 9x + 1

• 4x - 2x - 8 = 2x + 8

• 5x - 8 + 6x = -x - 8

• 7x + 2x + 7 = 9x + 7

Which statement is false for any value of x?

• 7x + 2x + 7 = 9x + 7

• 7x + 2x - 1 = 9x + 1

• 4x - 2x - 8 = 2x - 8

• 3x + 10 - 3x = 10

Priya read X books and was invited to a party for reading at least 25 books. Which inequality represents this situation?

• X ≤ 25

• X ≥ 25

• X > 25

• X < 25

Kieran read X books but was not invited to the party. Which inequality represents this situation?

• X ≤ 25

• X > 25

• X ≥ 25

• X < 25

Which number line represents X is less than or equal to 25?

• A point above 25 colored in with an arrow to the left

• A point above 25 not colored in with an arrow to the right

• A point above 25 not colored in with an arrow to the left

• A point above 25 colored in with an arrow to the right

What information is needed to determine when a water bucket will be full?

• The rate of water flow and the temperature

• The size of the bucket and the time of day

• The rate of water flow and the size of the bucket

• The size of the bucket and the type of water faucet

If a water bucket is being filled at a constant rate, what do you need to know to solve when it will be full?

• The size of the bucket and the type of water

• The size of the bucket and the time it started filling

• The rate of water flow and the type of bucket

• The rate of water flow and the size of the bucket