Unit 4, Lesson 7
More Balanced Moves
Accelerated 7
Practice
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
Next to each arrow, describe what is done in each step.
Problem 4
Andre solves an equation, but when he checks his answer he notices that his solution is incorrect. He knows he made an error, but he can’t find it. Where is Andre’s error 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
Match each expression in the first list with an equivalent expression from the second list.
\(6(x+2y) - 2(y-2x)\)
\(2.5(2x+4y) - 5(4y-x)\)
\(4(5x-3y) - 10x + 6y\)
\(5.5(x+y) - 2(x+y) + 6.5(x+y)\)
\(7.9(5x+3y) - 4.2(5x +3y) - 1.7(5x +3y)\)
\(10(x-y)\)
\(10(x+y)\)
Problem 6
The height of the water in a tank decreases by 3.5 cm each day. When the tank is full, the water is 10 m deep. The water tank needs to be refilled when the water height drops below 4 m.
- Write a question that could be answered by solving the equation \(10-0.035d=4\).
- Is 100 a solution of \(10-0.035d>4\)? Write a question that solving this problem could answer.