About Solving for a Specified Variable:
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
#1:
Instructions: Solve for z.
a) a(b + z) = cz + q
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#2:
Instructions: Solve for p, then r, then t.
a) I = prt
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#3:
Instructions: Solve for q.
a) aq - z = bq + n
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#4:
Instructions: Solve for z.
a) $$\frac{z + c}{z + a}=m + q$$
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#5:
Instructions: Solve for a.
a) $$zn + bn=\frac{ac - dg}{a}$$
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Written Solutions:
#1:
Solutions:
a) $$z=\frac{q - ab}{a - c}$$
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#2:
Solutions:
a)$$p=\frac{I}{rt}$$
$$r=\frac{I}{pt}$$
$$t=\frac{I}{pr}$$
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#3:
Solutions:
a) $$q=\frac{z + n}{a - b}$$
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#4:
Solutions:
a) $$z=\frac{ma + qa - c}{1 - m - q}$$
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#5:
Solutions:
a) $$a=-\frac{dg}{zn + bn - c}$$
