# Solving Equations (Lesson 6) OPTIONAL

## Drills

The triangle and the square have equal perimeters.

- Find the value of x.
- What is the perimeter of each of the figures?

Ask groups to share their strategies for solving the question. Consider asking some of the following questions:

- “What expression represents the perimeter of the triangle? The perimeter of the square?” (The expression for perimeter of the triangle is 5x−8, and the perimeter of the square is 4(x+2).)
- “What was your strategy in making an equation?” (If both perimeters are the same, we can say their expressions are equal.)
- “What does x mean in the situation?” (It means an unknown value. None of the sides or perimeter is represented by x, so we cannot say it represents a specific thing on the figures.)
- “Looking at the figures, are there any values that x could not be? Explain your reasoning.” (Since the triangles have sides that are 2x, x cannot be 0 or a negative value. Triangles cannot have sides with 0 or negative side lengths. Since the third side is x−8, we can use this same reasoning to realize that x must actually be greater than 8.)
- “How does this information help when solving?” (If I make a mistake in my solution and get a value of x that is less than or equal to 8, then I know immediately that my answer is not reasonable and I can try to find my error.)

*Conceptual Processing: Processing Time.*Begin with a demonstration of the first equation, which will provide access for students who benefit from clear and explicit instructions.Without solving, identify whether these equations have a solution that is positive, negative, or zero.

- x6=3x4
- 7x=3.25
- 7x=32.5
- 3x+11=11

- 9−4x=4
- -8+5x=-20
- -12(-8+5x)=-20