In this lesson, you are going to use the same process as before with solving equations.
Literal Equations are equations (formulas specifically) which will have more than one variable, or letter, and usually will not have any numbers.
Example #6
Suppose you are given the formula for the area of a rectangle, A = lw The area of a rectangle is the product of the length and the width. .
Rewrite this equation in terms This means "to solve". So, in this example, we are going to solve for the length of l.
We have A =lw and we and to solve for l. Let's rewrite this formula with multiplication.
A = l × w
You can see we have l multiplied by w. To move w (since we are solving for l), you will need to apply the inverse operation of multiplication. What is this inverse operation of multiplication?
Multiplication or Division
To solve for l, you determined that division should be the first step. Let's divide on both sides by w.
When you divide on both sides by w, you will be left with l on the right-hand side and the quotient of the area and width on the left-hand side. Or, more precisely:
Example #7
Obviously, all equations will not be as easy as that equation. Let's think about the equation y = mx + b. Suppose you want to solve for b.
If you want to solve for b, then you simply have to move the mx from the right-hand side. Which operation could we apply?
Addition
Subtraction
Multiply
Divide
Solve the equation y = mx + b for the variable b.
We are going to subtract mx from both sides.
After you subtract mx from both sides, ask yourself, "Are y and mx considered like terms?" Choose your answer below.
Yes
No
Since y and mx are not like terms, they cannot be combined. Therefore, they will simply be subtracted after y.
y - mx = b
Now that you have b = y - mx, you're done.
Example #8
Think about the same equation y = mx + b. However, in this example, solve the equation for x.
By now, you should see that you need to move the mx term first. Do this now.
y and b are not like terms, so they cannot be combined.
y - __ = mx
Since y and b are not like terms, you will find that you have y - b on the left-hand side.
Think about the same equation y = mx + b. However, in this example, solve the equation for x.
If you are solving for x, determine which variable would need to be moved next.
x or m
Think about the same equation y = mx + b. However, in this example, solve the equation for x.
We have m multiplied by x, so which inverse operation will we use?
Addition
Subtraction
Multiplication
Division
Think about the same equation y = mx + b. However, in this example, solve the equation for x.
We are going to apply the division property as the inverse operation for multiplication. Therefore, divide both sides by m.
Be careful, because the entire left-hand side must be divided by m. On the right-hand side, the m in the numerator and m in the denominator will cancel.
When you simplify the equation, you should have your answer.
Example #9
Given the equation A = P + Prt, solve the formula for r.
Since you are solving for r, you should move the first P to the other side. What will remain on the left-hand side?
__ - __ = Prt
Next, divide on both sides by anything not needed on the right-hand side.
On the right-hand side, Pt will cancel. Then, you are left with your answer.
Example #10
Solve bx – c = d for x.
If you want to solve for x, do not move x. We must get rid of the adding and subtracting first.
How do we undo subtraction?
If we want x by itself, how do we get rid of multiplication?
Now that we have x by itself, so we are finished!
