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**Solving Literal Equations**

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**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.

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**This process of solving a formula for a given**

variable is called "solving literal equations".

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**One of the dictionary definitions of "literal"**

is "related to or being comprised of letters“. Variables are sometimes referred to as literals.

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**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.”

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**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.

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**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?

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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’?

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**P=4s That’s right, you have to divide by ‘4’. You**

also have to remember to divide both sides by 4.

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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.

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**Let’s look at another example:**

2Q - c = d Multiply both sides by 2. Subtract ‘c’ from each side.

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**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’.

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**Work the following on your paper.**

d = rt Solve for ‘r’

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Check your answer. d = rt for ‘r’

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**Work the following on your paper.**

P = 2l +2w Solve for ‘w’

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Check your answer. P = 2l +2w for ‘w’

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**Work the following on your paper.**

Solve for ‘t’

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Check your answer. for ‘t’

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**Work the following on your paper.**

mx + 4y = 3t Solve for x

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

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**Work the following on your paper.**

Solve for b

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Check your answer. solve for b

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**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.

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Check your answer. solve for r

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**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)

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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)

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**examples around the room.**

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

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