1. Solving Literal Equations

2. Sometimes you have a formula and you
need to solve for some variable other than
the "standard" one.
Example: Perimeter of a square
P=4s
It may be that you need to solve this
equation for s, so you can plug in a
perimeter and figure out the side length.

3. This process of solving a formula for a given
variable is called "solving literal equations".

4. One of the dictionary definitions of "literal"
is "related to or being comprised of letters“.
Variables are sometimes referred to as
literals.

5. So "solving literal equations" may just be
another way of saying "taking an equation
with lots of variables, and solving for one
variable in particular.”

6. To solve literal equations, you do what
you've done all along to solve equations,
except that, due to all the variables, you
won't necessarily be able to simplify your
answers as much as you're used to doing.

7. Here's how "solving literal equations" works:
Suppose you wanted to take the formula for
the perimeter of a square and solve it for ‘s’
(or the side length) instead of using it to
solve for perimeter.
P=4s
How can you get the ‘s’ on a side by itself?

8. P=4s
Just as when you were solving linear
equations, you want to isolate the variable.
So, what do you have to do to get rid of the
‘4’?

9. P=4s That’s right, you have to divide by ‘4’. You
also have to remember to divide both sides
by 4.

10. This new formula allows us to use the perimeter formula to find the length of the sides of a square if we know the perimeter.

11. Let’s look at another example:
2Q - c = d
Multiply both sides by 2.
      
Subtract ‘c’ from each side.

12. As you can see, we sometimes must do
more that one step in order to isolate the
targeted variable.
You just need to follow the same steps that
you would use to solve any other ‘Multi-Step
Equation’.

13. Work the following on your paper.
d = rt
Solve for ‘r’

14. Check your answer.
d = rt for ‘r’

15. Work the following on your paper.
P = 2l +2w
Solve for ‘w’

16. Check your answer.
P = 2l +2w for ‘w’

17. Work the following on your paper.
Solve for ‘t’

18. Check your answer.
for ‘t’

19. Work the following on your paper.
mx + 4y = 3t
Solve for x

20. Check your answer.
mx + 4y = 3t, solve for x

21. Work the following on your paper.
Solve for b

22. Check your answer.
solve for b

23. Work the following on your paper.
In uniform circular motion, the speed v of a point on the edge of a spinning disk is where r is the radius of the
disk and t is the time it takes the point to travel once around the circle.
SOLVE the formula for r.

24. Check your answer.
solve for r

25. Suppose a merry-go-round is spinning once every 3 seconds. If
Use the previous slide.
Suppose a merry-go-round is
spinning once every 3 seconds. If
a point on the outside edge has a
speed of feet per second,
what is the radius of the merry-go-
round? (use 3.14 for pi)

26. Check your answer.
Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outside edge has a speed of feet per second, what is the radius of the merry-go-round? (use 3.14 for pi)

27. examples around the room.
Now you will solve some
REAL WORLD
examples around the room.