8. Literal Equations and Dimensional Analysis
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Apply inverse operations to isolate a.
a=- c/13
To solve the given literal equation for a, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.
LHS+8a=RHS+8a
LHS-c=RHS-c
.LHS /13.=.RHS /13.
Put minus sign in front of fraction
Rearranging an equation can often be very helpful when working in a subject other than math, such as physics, chemistry, carpentry, or baking. If you know every value except for one, substituting the values into one expression and simplifying to find the missing value is a lot faster than solving each time.
Imagine that we were commissioned to paint a mural. We were told that the exact required area A of our painting should be 50ft^2 but we were not told how long or wide it should be. We can use the formula for area of a rectangle to play around with various possible dimensions. However, it is much easier to do this with the formula rewritten a little bit. A=l w ⇔ l=A/w 50=l w ⇔ l=50/w Now we can substitute possible widths into the equation and find the corresponding lengths.
| Possible Width | Substitution | Corresponding Length |
|---|---|---|
| w= 10ft | l=50/10 | l= 5ft |
| w= 20ft | l=50/20 | l= 2.5ft |
| w= 30ft | l=50/30 | l= 1.6ft |