Lesson 20

Combining Like Terms (Part 1)

Let's see how we can tell that expressions are equivalent.

Problem 1

Andre says that \(10x+6\) and \(5x+11\) are equivalent because they both equal 16 when \(x\) is 1. Do you agree with Andre? Explain your reasoning.

Problem 2

Select all expressions that can be subtracted from \(9x\) to result in the expression \(3x+5\).

A:

\(\text-5+6x\)

B:

\(5-6x\)

C:

\(6x+5\)

D:

\(6x-5\)

E:

\(\text-6x+5\)

Problem 3

Select all the statements that are true for any value of \(x\).

A:

\(7x + (2x+7) = 9x+7\)

B:

\(7x + (2x - 1) = 9x + 1\)

C:

\(\frac12 x+(3 - \frac12 x)=3\)

D:

\(5x - (8 - 6x) =\text-x-8\)

E:

\(0.4x - (0.2x+8) =0.2x-8\)

F:

\(6x - (2x -4)=4x+4\)

Problem 4

For each situation, would you describe it with \(x< 25\), \(x > 25\), \(x \leq 25\), or \(x \geq 25\)?

  1. The library is having a party for any student who read at least 25 books over the summer. Priya read \(x\) books and was invited to the party.
  2. Kiran read \(x\) books over the summer but was not invited to the party.
  3.  
    A number line with the numbers 0 through 50, in increments of 5, indicated. A closed circle is indicated at 25 and an arrow is drawn from the closed circle extending to the left.
  4.  
    A number line with the numbers 0 through 50, in increments of 5, indicated. An open circle is indicated at 25 and an arrow is drawn from the open circle extending to the right.
(From Unit 6, Lesson 13.)

Problem 5

Consider the problem: A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?

(From Unit 2, Lesson 9.)