# Lesson 16

Rewriting Equations for Perspectives

- Let’s match and rewrite linear equations.

### 16.1: No Bad Apples

Which option would you select? Use mathematical reasoning to explain your selection.

Option A: Each apple costs $0.97 and are on sale with a “Buy 2, Get 1 Free” offer.

Option B: Bags of 6 apples are on sale “2 for $7.50” but you must buy 2 bags.

### 16.2: A Charity Shopping Trip

A person has collected a lot of money for providing clothing to those in need. They go to a store to buy several clothing items with the money collected.

Match each description in column A with an equation from column B that represents the situation. Be prepared to explain your reasoning.

- Take turns with your partner to match a description of a situation with an equation that represents the situation.
- For each match that you find, explain to your partner how you know it’s a match.
- For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

- A store charges $6 for each shirt sold. A person buys \(x\) shirts and pays \(y\) dollars for the total.
- A store charges $6 for each pair of shorts sold. They also offer a $3 coupon to be used on the entire order. A person buys \(x\) pairs of shorts and pays \(y\) dollars for the total after using the coupon.
- A store charges $6 for 3 pairs of socks. A person buys \(x\) pairs of socks and pays \(y\) dollars for the total.
- A store charges $6 for each pair of shoes sold and also charges $3 to lace up all of the shoes in the entire order. A person buys \(x\) pairs of shoes and pays \(y\) for the total including lacing up all the shoes.
- A store charges $3 for 6 handkerchiefs. A person buys \(x\) handkerchiefs and pays \(y\) for the total.
- A store charges $3 for each pair of gloves sold. They also offer a $6 coupon to be used on the entire order when there are more than 4 pairs of gloves purchased. A person buys \(x\) pairs of gloves (with \(x > 4\)) and pays \(y\) dollars for the total after using the coupon.

- \(y = 6x\)
- \(y = \frac{6x}{3}\)
- \(y = \frac{3x}{6}\)
- \(y = 3x - 6\)
- \(y = 6x - 3\)
- \(y = 6x + 3\)

### 16.3: Isolate the $x$

Rearrange the equations so that one side of the equation is only \(x\). Be prepared to explain or show your reasoning.

- \(T = x - 2\)
- \(T = 2x\)
- \(T = 2x - 1\)
- \(T = \frac{x}{2}\)
- \(T = 2(x-1)\)
- \(T = \frac{x-1}{2}\)