Section A Section A Checkpoint

Problem 1

Label the arrows to describe the moves that create equivalent equations.
Are these 2 equations equivalent? Explain your reasoning.

$\begin{align} 4x + 2 &= 20x\\ x + 2 &= 5x \end{align}$

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Solution

Add 3, distributive property
No. Sample reasonings:
- Each term on the left should be divided by 4, but the 2 was not divided.
- The solutions are not the same. For the second equation, the solution is $x = \frac{1}{2}$ , but that does not solve the first equation because $4 \boldcdot \frac{1}{2} + 2 \neq 20\boldcdot \frac{1}{2}$ .

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Sample Response

Add 3, distributive property
No. Sample reasonings:
- Each term on the left should be divided by 4, but the 2 was not divided.
- The solutions are not the same. For the second equation, the solution is $x = \frac{1}{2}$ , but that does not solve the first equation because $4 \boldcdot \frac{1}{2} + 2 \neq 20\boldcdot \frac{1}{2}$ .

Solve the equation. Show your reasoning by describing any moves that you make to write equivalent equations.

$4(3 - x) = 3x-2$

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Solution

Sample response:

$12 - 4x = 3x - 2$ , I applied the distributive property

$12 = 7x - 2$ , I added $4x$ to each side

$14 = 7x$ , I added 2 to each side