In many cases, we are given a formula that describes a very specific relationship between two or more variables. In order to manipulate these formulas, it is necessary to solve a given formula for different variables. The key is to understand how to isolate any variable in an equation.
Test Objectives:•Demonstrate a general understanding of how formulas work
•Demonstrate the ability to extract information from a formula based on given inputs
•Demonstrate the ability to solve a formula for a given variable
Solving for a Specified Variable Test:
#1:
Instructions: Solve for z.
a) a(b + z) = cz + q
#2:
Instructions: Solve for p, then r, then t.
a) I = prt
#3:
Instructions: Solve for q.
a) aq - z = bq + n
#4:
Instructions: Solve for z.
a) $$\frac{z + c}{z + a} = m + q$$
#5:
Instructions: Solve for a.
a) $$zn + bn = \frac{ac - dg}{a}$$
Written Solutions:
Solution:
a) $$z = \frac{q - ab}{a - c}$$
Solution:
a) $$p = \frac{I}{rt}$$
$$r = \frac{I}{pt}$$
$$t = \frac{I}{pr}$$
Solution:
a) $$q = \frac{z + n}{a - b}$$
Solution:
a) $$z = \frac{ma + qa - c}{1 - m - q}$$
Solution:
a) $$a = -\frac{dg}{zn + bn - c}$$