Simple Literal Equations

Solving Literal Equations

With Review

A Literal equation is easy if you know your basic operations and how to apply them to equations.

By now you know the basics,

but let us review.

You have your basic one step equations where you use the opposite operator to solve for the variable.

Always maintain balance by doing the same operation to both sides.

When you have more than one step to do, start by adding or subtracting any constants by themselves.

Then follow that with multiplying and dividing to isolate the variable.

Sometimes you have a variable on both sides of the equation.

you can add and subtract variables just like constants. I suggest always starting with the smaller coefficient. notice 3 is smaller than 5, so we can subtract 3x from both sides. Then it becomes an easy two step equation. Try a few for practice.

Multiple Choice

What should you do first?

5X - 3 = 2X + 4

• Subtract 2 from both sides

• Subtract 2X from both sides

• Add 2X to both sides

• Subtract 5X from both sides

Multiple Choice

What should you do first?

3X + 2 = -4X -5

• Subtract 3X from both sides

• Add 4X to both sides

• Add 3X to both sides

• Subtract 4X to both sides

Did you get those right?

The correct answer was starting with the smaller coefficient. In the first question, 2X had the smaller coefficient, In the second question, -4X was smaller. Remember negative numbers are smaller.

Secret: You solve them the same way as other equations.

A Literal equation contains at least two different variables.

Before you had one variable and you isolated it to get a numerical answer. In literal equations you still want to isolate a variable, just the answer will contain the other variables as well. Notice in the picture X and Z are isolated and all other variables and constants are on the other side of the equal sign.

You have seen literal equations before represented as Math formulas.

What are some formulas you remember?

Here we have a literal equation already solved for H.

But what if we want to solve for A?

we can use the same opposite operations method we have been using to achieve this.

Our goal to get A by itself on one side of the equal sign and everything else on the other side.

on the next slide we will go over this step by step.

Let us begin our process of getting A isolated.

Just as if this was 5=3x+4, we would start by -4 from both sides; we can

-r from both sides the same way. Then in the previous example we would divide by 3 from both sides; we can divide B from both sides. Now we know what A equals. Remember to only combine like terms. you will notice in literal equations, there are not many.

Examine these two literal equations.

Sometimes there are numbers and sometimes there are only variables.

The first one went from A= to B=:

start by multiply both sides by D, then dividing both sides by C.

The second one went from X= to T=:

start by subtracting 3W from both sides, then dividing both sides by 2.

Why do we even need this?

Some common literal equations involve converting temperature from celsius to fahrenheit or vice versa. There are also lots of literal equations in geometry. They will save you time.

Maybe you should try a few yourself.

Use paper and pencil if needed.

Multiple Choice

Solve for A

$$\frac{a}{b}=h$$  

• $$a=bh$$  

• $$a=\frac{b}{h}$$  

• $$a=\frac{h}{b}$$  

Multiple Choice

Solve for C

$$\frac{ca}{k}+e=s$$  

• $$c=aesk$$  

• $$c=\frac{kes}{a}$$  

• $$c=\frac{k\left(s-e\right)}{a}$$  

• $$c=\frac{\left(s-e\right)}{ak}$$  

How do you know when you have solved a literal equation?

What would it look like?

Remember the distributive property?

We can distribute that 4 into each term inside the parenthesis. Did you know you can go backwards and un-distribute the 4 too. This is called factoring and is part of the distributive property. If we distributed the 4 with multiplication, then factoring is like dividing the 4 out of each term.

Let us use the distributive property with Literal equations to solve for X.

Notice we start simplifying like any other equation, but end up with

AX-2X=5B. We want only one X, and AX and -2X and not like terms. We can use the distributive property to factor out the X. Now we have one X and can solve for X. try one.

Multiple Choice

Solve for B.

A = BC + BD

• B = (ACD)

• B = (A - CD)

• B=A/(C+D)

• B=A/(CD)

Poll

How do you feel about solving equations?

• I got this, it is easy.

• I will feel better after I practice by finishing my homework.

• I understand the basics

• I need to ask you for more help