Miscellaneous Notes

$a - x = b$ | $-a$
$-x = -a + b$ | $\times -1$
$x = a - b$

$\frac 3 2 x$ are one term -> $\frac {3x}{2}$

$\frac {7x}{8} - (x-2) = 12$ -> Distribute before multiplying by LCD
$\frac {7x}{8} - x + 2 = 12$

$\frac {24x-60}{3} - \frac {36x -12}{4}$ -> Distribute before adding or subtracting
$\frac {24x-60} + \frac {-36x + 12}{4}$

Square roots

$\frac {16T}{\pi f} = d^3$ solved for $d$: $d = \sqrt[3]{\frac {16T}{\pi f}}$

If the solution can be either positive or negative: $x = \sqrt[\pm]{a+b}$

Multiplication of terms in algebra

$210 = \frac 1 2 (3T-1)T$ | $* 2$
$420 = (3T-1)T$
$420 = 3T^2-T$

Solve for $d$:
$L = L + \frac {8d^2}{3C}$ | $* 3C$
$3CL = 3C^2 + 8d^2$

Solve for V: $h = 0.03 \frac L D \times \frac {V^2}{2g}$ (multiply by $D2g$)
$0.03LV^2 = 2gDH$