Lesson 9

Combining Like Terms (Part 1)

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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.

Solution

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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:

\(\text-6x+5\)

Solution

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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:

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

Solution

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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.

Solution

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(From Unit 4, Lesson 3.)

Problem 5

A line is represented by the equation \(\frac{y}{x-2}=\frac{3}{11}\). What are the coordinates of some points that lie on the line? Graph the line on graph paper.

Solution

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(From Unit 2, Lesson 17.)

Problem 6

Select all the statements that must be true for any scaled copy Q of Polygon P.

Angle measures of Polygon P clockwise from bottom left, in degrees, 90, 125, 35, 250, 80, 135.
A:

The side lengths are all whole numbers.

B:

The angle measures are all whole numbers.

C:

Q has exactly 1 right angle.

D:

If the scale factor between P and Q is \(\frac15\), then each side length of P is multiplied by \(\frac15\) to get the corresponding side length of Q.

E:

If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.

F:

Q has 2 acute angles and 3 obtuse angles.

Solution

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(From Unit 2, Lesson 3.)