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Author:
Todd Parks

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Tutorial

**Student Outcomes**

- Students use tape diagrams to solve equations of the form
*px + q = r*and*p(x + q) = r*, (where*p, q*, and*r*, are*small positive*integers), and identify the sequence of operations used to find the solution. - Students translate word problems to write and solve algebraic equations using tape diagrams to model the steps they record algebraically.

**Lesson Questions**

- How does modeling the sequence of operations with a tape diagram help to solve the same problem algebraically?

- What are the mathematical properties, and how are they used in finding the solution of a linear equation containing parenthesis?

**Lesson Summary**

- Tape Diagrams can be used to model and identify the sequence of operations to find a solution algebraically.
- The goal in solving equations algebraically is to isolate the variable.
- The process of doing this requires “undoing” addition or subtraction to obtain a 0 and “undoing” multiplication or division to obtain a 1. The additive inverse and multiplicative inverse properties are applied, to get the 0 (the additive identity) and 1 (the multiplicative identity).
- The addition and multiplication properties of equality are applied because in an equation, A = B, when a number is added or multiplied to both sides, the resulting sum or product remains equal.