Some common equations you see all over the place:

• Direct Variation

y = kx

y and x move in proportion with one another. The constant of proportionality is k

• Inverse cariation

y = k/x

y and x move inverse with one another

• Decimal equations

.1x + .02 = .004 multiply by 1000 100x + 20 = 4

• Fractional equations

To clear a fraction from an equation, multiply both sides by the reciprocal (or common denominator of all fractions)

• Rational equations

Ex: Solve for a

4/x + (6/x+a) = 1

Common denominator is x(x+a)

[4/x + (6/x+a) = 1](x(x+a))

4(x+a) + 6x = x(x+a)

4x + 4a + 6x = x^2 + ax

4a - ax = x^2 - 10x

a(4-x) = x^2 - 10x

a = (x^2 - 10x)/(4 - x)

• Radical equations

sqt(x-2) - 6 = 0
sqt(x-2) = 6
x-2 = 36
x = 38

When simplifying a quadratic you may introduce extraneous solutions, so you must plug in your answers and check. This happens because if you take 1^2 or -1^2 you get 1, so a radical equation is one interpretation, the positive square root. This means you lose some information and introduce an extraneous solution.

sqt(x) != +-sqt(x)

• Multi variable equations

Just isolate the variable you are solving for.

Example: distance = rate * time