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Lesson 1.5 “Rewriting Equations and Formulas”
Lesson 1.5 “Rewriting Equations and Formulas”
Essential Question: How can you use a formula for one measurement to write a formula for a
different measurement? Why would you even do this?
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What do you already know about solving for a particular variable in a linear equation or formula?
Solution of the equation: ________________________________________________________________
A literal equation means that the equation has ______________________________________________
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*In order to move variables around in a formula, to solve for the given variable, you would remember to
use inverse operations. Every time you move a variable or number from one side of the equal sign to
the other side, use your inverse operations.
Example:
Solve the literal equation y = 2x + 4 for x.
First, look at the equation…what needs to move, what stays in place? You need everything to equal x, or
x to equal everything.
Second, I see the x is on the right side…I also see I can easily move the “4” to the other side (working to
get x by itself). If “4” is being added, I’m going to subtract “4” from both sides.
y = 2x + 4
-4
-4
y – 4 = 2x
Now I almost have x by itself. My final step would be to separate the “2” and the x. Since they are
sitting beside each other, I know they are being multiplied. My inverse would be division. So I’m going
to divide both sides of the equation by “2” to get x by itself.
y – 4 = 2x
2
2
𝒚𝒚 − 𝟒𝟒
= 𝒙𝒙
𝟐𝟐
You now transformed your original equation of y = 2x + 4 to:
𝒚𝒚 − 𝟒𝟒
= 𝒙𝒙
𝟐𝟐
Example #2:
Solve the literal equation w = 4x + xy – 2 for x.
First, look at the equation…what needs to move, what stays in place? You need everything to equal x, or
x to equal everything.
Second, I see “x” is being used in two different ways on the right side of the equation. So…I need to
factor the “x” out, leaving what is left in parentheses, since he is in common with two different terms.
Make sure you leave the “-2” alone, because does not use an “x”.
w = 4x + xy - 2
w = x(4 + y) - 2
Now I have “x” kind of by itself. My next to last step would be to add the “-2” to both sides. Since they
w = x(4 + y) - 2
+2
+2
w + 2 = x (4 + y)
Your final step is to now get the “x” completely be himself. To do so, I see the “x” and (4 + y) are sitting
beside each other, which means I know they are being multiplied. My inverse would be division. So I’m
going to divide both sides of the equation by “(4 + y)” to get x by itself.
You now transformed your original equation of w = 4x + xy – 2 to:
𝒘𝒘 + 𝟐𝟐
= 𝒙𝒙
𝟒𝟒 + 𝒚𝒚
Practice:
1.
Solve the literal equation 4x – 7y = 12, for y.
2. Solve the literal equation 3w + 4wp = a, for w.
3. The formula for the area of a circle is A = πr2. Solve the formula for r.
4.
A patio is in the shape of a parallelogram. Its base, which is up against the side of the house, is
13 feet. The area of the patio is 156 square feet. The height of the parallelogram represents the
distance from the house to the edge of the patio. The yard is 24 yards deep from the house to
the back fence. Draw a picture of this to help you.
a. Find the distance from the house to the edge of the patio.
b. How far is it from that edge of the patio to the back fence?