**Objectives**

- Solve literal equations with two variables.
- Rearrange formulas to solve for a quantity of interest in a real-world problem.
- Describe the steps in solving equations.
- Use units to guide and interpret your solutions of literal equations and formulas.

**Key Terms**

- Fahrenheit and Celsius – Ways to calculate and tell the temperature.
- In the USA, we use Fahrenheit. In Europe (and many other countries), they use Celsius.
- Formula for finding Celsius:
- What if you wanted to solve for Fahrenheit instead?
- Try solving for F by doing inverse (reverse) operations until you isolate the F.
- Step 1: Multiply by 9 on both sides of the equation
- and this will give you:

- Step 2: Divide by 5 on both sides of the equation
- and this will give you:

- Step 3: Add 32 to both sides of the equation
- You get the formula for finding Fahrenheit:
- You can rewrite it as

- Formula – An equation that describes an important mathematical relationship.
- Literal Equation – An equation that involves two or more variables.
- Ohm’s Law – Describes the relationships among voltage, current, and resistance in a conductor (ex. computer circuits)
- The voltage of the current is
*V*. - The amount of current flowing through the conductor is
*I* - Any resistance that is present is measured with R
*Formula: V*=*IR*- Example: If a voltage of 0.5 V (volts) is driving a current of 0.03 A (amps) through a resistor, what is the resistance fo the resistor, measured in ohms?
- The symbol for ohms is Omega:
- Step 1: List what we know and the formula
- V: 0.5
- I: 0.03
- Formula: V = IR
- Variable (unknown): R

- Step 2: Solve for R by dividing by I on both sides to isolate R
- Step 3: Substitute and solve
- The resistance of a computer circuit is 16.667 ohms

- The voltage of the current is

- Perimeter – The distance around an object
- Perimeter of a rectangle (formula):
*P*= 2*l*+ 2*w*- P = perimeter
- l = length
- w = width

- Perimeter Example: Felicia has 60 feet of fencing. She’d like to use all of this fencing to enclose a rectangular space in her backyard for a vegetable garden. The length of the garden must be 10 feet. What will the width be?
- Step 1: List the facts & formula
*P*= 2*l*+ 2*w*- Perimeter (fencing): 60ft
- Space: rectangular
- length: 10ft
- width: ?

- Step 2: Solve for w
- Step 3: Substitute known variables
- Step 4: Simplify and solve
- w = 20
- The width of the garden is 20 feet long.

- Step 1: List the facts & formula

- Perimeter of a rectangle (formula):

**Notes**

- Literal Equation Example 1: Solve for y
- Step 1: Write the problem
- Step 2: Subtract 20x on both sides
- Step 3: Divide both sides by 5
- Step 4: Separate the fraction on the right side into two terms
- Step 5: Simplify

- Step 1: Write the problem

- Literal Equation Example 2: Solve for x
- Step 1: Write the problem
- Step 2: Subtract 5y on both sides
- Step 3: Divide both sides by 20
- Step 4: Separate the fraction on the right side into two terms
- Step 5: Simplify

- Step 1: Write the problem