1. Solving Linear Equations

A linear equation has a variable raised only to the power of 1 (no \(x^2\), no \(\sqrt{x}\)). The goal is always the same: isolate the variable on one side.

The Golden Rule: whatever you do to one side, you must do to the other.

Worked example: Solve \(2x + 5 = 13\).

Step 1 - Subtract 5 from both sides to undo the "+5":
\[ 2x + 5 - 5 = 13 - 5 \;\Rightarrow\; 2x = 8 \]

Step 2 - Divide both sides by 2 to undo the "times 2":
\[ \frac{2x}{2} = \frac{8}{2} \;\Rightarrow\; x = 4 \]

Step 3 - Check by substituting back: \(2(4) + 5 = 8 + 5 = 13\). Correct.

Tip: Always do the opposite operation (inverse). Addition undoes subtraction; multiplication undoes division.