# Lesson 16

Rewriting Equations for Perspectives

• Let’s match and rewrite linear equations.

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.

1. Take turns with your partner to match a description of a situation with an equation that represents the situation.
1. For each match that you find, explain to your partner how you know it’s a match.
2. For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
1. A store charges $6 for each shirt sold. A person buys $$x$$ shirts and pays $$y$$ dollars for the total. 2. 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. 3. A store charges$6 for 3 pairs of socks. A person buys $$x$$ pairs of socks and pays $$y$$ dollars for the total.
4. 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.
5. A store charges $3 for 6 handkerchiefs. A person buys $$x$$ handkerchiefs and pays $$y$$ for the total. 6. 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.

1. $$T = x - 2$$
2. $$T = 2x$$
3. $$T = 2x - 1$$
4. $$T = \frac{x}{2}$$
5. $$T = 2(x-1)$$
6. $$T = \frac{x-1}{2}$$