### 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:

$$p = \frac{I}{rt}$$

$$r = \frac{I}{pt}$$

$$t = \frac{I}{pr}$$

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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) $$a = -\frac{dg}{zn + bn - c}$$