Bell Ringer

1. What is the solution of 2b + 3b + 6 = 21?2. Verify that the solution to the equation

below is correct. Then justify each step that was used to solve the equation. (Example of step used might be distribution, simplification, addition, multiply, etc.)8m + 6m − 12 = 72 – Step Used:2a) _________________14m − 12 = 72 – Step Used:2b) _________________14m = 84 – Step Used:2c) _________________m = 6 – Step Used:2d) _________________

Agenda & News

Start Literal Equations Assignment Ticket Out

First holiday, Monday, September 7th Labor day – No School

Rules to Remember

When solving an equation, the goal is to get the variable by itself.

Addition and Subtraction are inverse operations. (opposites)

Multiplication and Division are inverse operations. (opposites)

Don’t Forget

The equation is like a balance scale. Whatever you do to one side of the equation must be done to the other side of the equation.

New Vocabulary

Literal Equation – involves 2 or more variables. The equation is called literal because the coefficients and constants are replaced with letters.

Ex: 3x + 2y = 6

This equation can be solved for either x or y. (We will be told which one to solve for).

Literal Equations When you rewrite literal equations, you may have to

divide by a coefficient, a variable, or a variable expression.

A formula is a special type of literal equation because it involves two or more variables.

Here are other Literal Equations (or formulas)that you may have seen before:

P = 2L + 2Wd = rtA = bh

You can solve for any of the variables in any of these equations.

Solve it!1. You are ordering pizzas

and sandwiches. You have a budget of $80. How many sandwiches can you buy if you buy 4 pizzas?

2. What about 5 pizzas? Explain your answer.

1. Px + Sy = 80 10x+5y = 8010(4) + 5y = 80 40+5y=80 40-40+5y=80-40 5y = 40 y= 82. px + sy = 80 10x+5y = 8010(5) + 5y = 80 50+5y=80 50-50+5y=80-30 5y = 30 y= 6

Explain it!

As the number of pizzas

increases, the number of

sandwiches decreases.

Rewriting a literal equation In the last problem we solved

question 1 and 2 by substituting each x into the equation and then solving for y twice, once for each x-variable.

However, if you rewrite the equation first, you only have to isolate y once. Then substitute for x.

Redo

1. You are ordering pizzas and sandwiches. You have a budget of $80. How many sandwiches can you buy if you buy 3 pizzas?

2. What about 6 pizzas?

10x + 5y = 8010x + 5y – 10x = 80 – 10x 5y = 80 – 10x y = 16 – 2x

Step 2Step 1 Use the rewritten equation to find

y when x = 3 and when x = 6

y= 16 – 2x y= 16 – 2x y= 16 – 2(3) & y= 16 – 2(6)y= 10 y = 4

Key Understanding When you work with literal

equations, you can use the methods we have learned to isolate any particular variable.

Got it? #1 Solve the equation 4 = 2m – 5n for

m. What are the values of m, when n = -2, 0, and 2?

Rewriting literal equations Rewriting literal equations with only

variables When a literal equation contains only

variables, treat the variables you are not solving for as constants.

https://media.pearsoncmg.com/curriculum/math/ma_hs16tx_a1te/scos/A0262864/player.html

Got it? #2

What equation do you get when you solve –t = r + px for x?

-t = r + px -t – r = r + px – r -t – r = px = = x

Rewriting a formula

The formula for the Perimeter of a Rectangle isP = 2L + 2W

Example: Solve for W P = 2L + 2W

– 2L –2L P – 2L = 2W

P – 2L = 2W 2 2 P – 2L = W

2

L

W