Lesson 13

More Balanced Moves

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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:
\(\frac25b+1=\text-11\)
\(2b+1=\text-55\)
\(2b=\text-56\)
\(b=\text-28\)

 

Solution

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Problem 2

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

Solution

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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. \(x=\frac{6}{11}\)

Solution

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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?

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

 

Solution

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