Lesson 04: More Balanced Moves | Unit 4: Linear Equations and Linear Systems

Open Ended

Mai and Tyler work on the equation $$\frac25b+1=-11$$ together. Mai's solution is $$b=-25$$ and Tyler's is $$b=-28$$ . Here is their work. Do you agree with Mai's solution? Explain or show your reasoning. Mai: $$\frac25b+1=-11$$ $$\frac25b=-10$$ $$b=-10\cdot \frac52$$ $$b = -25$$

Open Ended

Mai and Tyler work on the equation $$\frac25b+1=-11$$ together. Mai's solution is $$b=-25$$ and Tyler's is $$b=-28$$ . Here is their work. Do you agree with Tyler's solution? Explain or show your reasoning. Tyler: $$\frac25b+1=-11$$ $$2b+1=-55$$ $$2b=-56$$ $$b=-28$$

Multiple Choice

What is the solution to $$3(x-4)=12x$$ ?

• 4
• -4/3
• 12
• -3

Multiple Choice

What is done in the first step of solving the equation 2(-3x + 4) = 5x + 2?

• Combine like terms.
• Add 5x to both sides.
• Distribute the 2.
• Subtract 2 from both sides.

Multiple Choice

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 in the following equation? What is the solution to the equation?

• -1
• -3
• 2
• 0

Multiple Choice

Elena and Lin are trying to solve $$\frac12x+3=\frac72x+5$$ . Describe the change Elena makes to each side of the equation. Elena’s first step is to write $$3=\frac72x-\frac12x+5$$ .

• Elena changes the equation to 3 = \frac{7}{2}x - \frac{1}{2}x + 5.
• Elena changes the equation to 3 = rac{7}{2}x - 5.
• Elena changes the equation to 3 = rac{7}{2}x + rac{1}{2}x + 5.
• Elena changes the equation to 3 = rac{1}{2}x + 5.

Multiple Choice

What change does Lin make to each side of the equation $$\frac12x+3=\frac72x+5$$ to get $$x+6=7x+10$$ ?

• Lin subtracts \frac{1}{2}x and 3 from both sides.
• Lin divides both sides by 2.
• Lin multiplies both sides by 2.
• Lin adds rac{1}{2}x and 3 to both sides.

Open Ended

Solve the equation $$3(x-5) = 6$$ . Explain or show your reasoning.

Open Ended

Solve the equation $$2(x-\frac{2}{3})=0$$ . Explain or show your reasoning.

Open Ended

Solve the equation $$4x - 5 = 2 -x$$ . Explain or show your reasoning.