1. Algebraic Expressions and Equation-Solving

Expressions name quantities; equations say two expressions are equal. The skill of algebra is manipulating both correctly.

Variable — a letter standing for an unknown number.
Term — a number, variable, or product of both. Like terms share the same variable(s) to the same power.

Combining like terms:
\[ 4x^2 - x + 3x^2 + 5x = 7x^2 + 4x. \]

Distributive property: multiply the outside factor by every term inside.
\[ -2(3x - 4) = -6x + 8. \]

Solving linear equations: use inverse operations to isolate the variable. Whatever you do to one side, do to the other.
\[ \frac{2}{3}x - 5 = 7 \quad\Rightarrow\quad \frac{2}{3}x = 12 \quad\Rightarrow\quad x = 18. \]

Equations with variables on both sides:
\[ 5x - 3 = 2x + 9 \quad\Rightarrow\quad 3x = 12 \quad\Rightarrow\quad x = 4. \]

Literal equations: rearrange a formula for a specific variable.
\[ I = Prt \quad\Rightarrow\quad P = \frac{I}{rt}. \]