# Lesson 4

More Balanced Moves

Let's rewrite some more equations while keeping the same solutions.

### 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.

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

### 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?

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

### Problem 5

Choose the equation that has solutions \((5, 7)\) and \((8, 13)\).

\(3x-y =8\)

\(y=x+2\)

\(y-x=5\)

\(y=2x-3\)

### Problem 6

A length of ribbon is cut into two pieces to use in a craft project. The graph shows the length of the second piece, \(x\), for each length of the first piece, \(y\).

- How long is the ribbon? Explain how you know.
- What is the slope of the line?
- Explain what the slope of the line represents and why it fits the story.