Literals Re-Intro

Literal Equations

Literal equations, simply put, are equations containing two or more variables. Your goal is to solve for just one variable with respect to others.

Key Strategy to Solve Literal Equations

• Isolate or keep by itself a certain variable on one side of the equation (either left or right) and the rest on the opposite side.

• If you know how to solve regular One-Step Equations, Two-Step Equations, and Multi-Step Equations, the process of solving literal equations is very similar.

• It’s just a matter of practice and familiarization.

Multiple Choice

Consider this one-step equation:

 $7=x-3$ 

What one step should be taken on both sides to "solve for x" ?

• add 3 on both sides

• subtract 7 to both sides

• subtract x from both sides

Multiple Choice

Now consider this equation:

 $7=x-y$  

 What one step should be taken on both sides to "solve for x" ?

• subtract x from both sides

• add y to both sides

• subtract 7 from both sides

Here's a two-step equation with a fraction:

Fractions are Division

Multiple Choice

This formula represents (S)peed in terms of (D)istance over (T)ime. 

 $S=\frac{D}{T}$       

Use the formula to answer the question.

How fast do I have to drive to get to NYC (336 miles away) in 4 hours.

•  $\frac{336\ miles}{4\ hours}=84mph$  

•  $\frac{4\ hours}{336\ miles}=84mph$  

Multiple Choice

84mph is speeding!

OK so, in an effort to not get a ticket our max speed is 70mph on most highways. So now we know how far and how fast we need to go. What can we do to figure out how much time we need to travel?

• Solve for S

• Solve for D

• Solve for T

Solving for (T)ime

Multiple Choice

 $S=\frac{D}{T}$                      $D\ =\ ST\ \$                     $T\ =\ \frac{D}{S}$  

We can solve for any variable we want in a given formula. Now, how long should it take to get to NYC (336 miles away) driving 70 mph?

•  $\frac{336\ mi}{4\ hr}=\ 84mph$  

•  $\frac{70\ mi}{hr}\cdot4hr=\ 128\ mi$  

•  $\frac{336\ mi}{70\ \frac{mi}{hr}}\ =4.8\ hr$  

Summary

• Literals are just one, two, or multistep equations with more than one variable

• Solving for variables allows us to manipulate formulas to fit our needs

• We will focus on this skill for the next few classes.

Poll

How well do you think you remember this from Algebra 1?

• I don't remember any of this.

• I remember this a little bit.

• I'm okay at solving literals.

• I'm awesome at solving literals.