Lesson 21: Combining Like Terms (Part 2) | Unit 6: Expressions, Equations, and Inequalities

Open Ended

Noah says that $$9x - 2x + 4x$$ is equivalent to $$3x$$ because the subtraction sign tells us to subtract everything that comes after $$9x$$ . Do you agree with Noah? Explain your reasoning.

Open Ended

Elena says that $$9x - 2x + 4x$$ is equivalent to $$11x$$ because the subtraction only applies to $$2x$$ . Do you agree with Elena? Explain your reasoning.

Multiple Choice

Identify the error in generating an expression equivalent to $$4+2x-\frac12(10-4x)$$ .

Then correct the error.

Which of the following steps contains the error?

$$4+2x + \frac {\text{-}1}{2}(10 + -4x)$$ $$4+2x +-5 +2x$$ $$4+2x-5+2x$$ $$-1$$

• 4 + 2x - 5 - 2x = -1
• 4 + 2x - 5 + 2x = 2x - 1
• 4 + 2x + 5 + 2x = 2x + 9
• 4 + 2x - 5 + 4x = 2x - 1

Multiple Select

Select all expressions that are equivalent to $$5x -15 - 20x+10$$ .

• $$5x - (15+20x) + 10$$

• $$5x+-15+-20x+10$$

• $$5(x-3-4x+2)$$

• $$-5(-x +3+4x+-2)$$

• $$-15x-5$$

Open Ended

Decide whether the expression 1 is equivalent to the expression 2. If they are not equivalent, show how to change one expression to make them equivalent.

Expression 1:
$$3x-2x+0.5x$$

Expression 2: $$1.5x$$

Multiple Choice

Decide whether the expression 1 is equivalent to the expression 2. If they are not equivalent, show how to change one expression to make them equivalent.

Expression 1:
$$3(x+4) - 2(x+4)$$

Expression 2: $$x+3$$

• No, they are not equivalent. Change Expression 2 to x + 4.
• Yes, they are equivalent. No changes needed.
• No, they are not equivalent. Change Expression 1 to 3(x+3).

Multiple Choice

Decide whether the expression 1 is equivalent to the expression 2. If they are not equivalent, show how to change one expression to make them equivalent.

Expression 1:
$$6(x+4)-2(x+5)$$

Expression 2: $$2(2x+7)$$

• Yes, the expressions are equivalent.
• No, they can only be made equivalent by changing the constants.
• Yes, but they need to be simplified further.

Multiple Choice

Are the following expressions equivalent?

Expression 1:

$$3(x+4) - 2(x+4) + 0.5(x+4)$$

Expression 2: $$1.5(x+4)$$

• Only Expression 1 is valid.
• Yes, the expressions are equivalent.

Multiple Choice

Decide whether the expression 1 is equivalent to the expression 2. If they are not equivalent, show how to change one expression to make them equivalent.

Expression 1:

$$20(\frac{2}{5}x + \frac{3}{4}y - \frac{1}{2})$$

Expression 2: $$\frac{1}{2}(16x + 30y - 20)$$

• Yes, the expressions are equivalent.
• They are equivalent if we ignore the constants.
• Yes, but only if we change the coefficients.
• No, the expressions are not equivalent.