# Lesson 13

More Balanced Moves

### Problem 1

Mai and Tyler work on the equation $$\frac25b+1=\text-11$$ together. Mai's solution is $$b=\text-25$$ and Tyler's is $$b=\text-28$$. Here is their work. Do you agree with their solutions? Explain or show your reasoning.

Mai:
$$\frac25b+1=\text-11$$
$$\frac25b=\text-10$$
$$b=\text-10\boldcdot \frac52$$
$$b = \text-25$$

Tyler:
$$\frac25b+1=\text-11$$
$$2b+1=\text-55$$
$$2b=\text-56$$
$$b=\text-28$$

### Problem 2

Solve $$3(x-4)=12x$$

### Problem 3

Describe what is being done in each step while solving the equation.

1. $$2(\text-3x+4)=5x+2$$
2. $$\text-6x+8=5x+2$$
3. $$8=11x+2$$
4. $$6=11x$$
5. $$x=\frac{6}{11}$$

### Problem 4

Andre solved an equation, but when he checked his answer he saw his solution was incorrect. He knows he made a mistake, but he can’t find it. Where is Andre’s mistake and what is the solution to the equation?

\displaystyle \begin{align} \text{-}2(3x-5) &= 4(x+3)+8\\\text{-}6x+10 &= 4x+12+8\\\text{-}6x+10 &= 4x+20\\ 10 &= \text{-}2x+20\\\text{-}10 &= \text{-}2x\\ 5 &= x\end{align}