Algebra & Variables

Multi-Step Equations

Solve by undoing operations in reverse order (PEMDAS reversed): first undo addition/subtraction, then multiplication/division.

Example: 3x − 7 = 14
Step 1: add 7 → 3x = 21
Step 2: divide by 3 → x = 7

Combining like terms: 2x + 5x = 7x  •  4a − a + 3 = 3a + 3

Inequalities

Solve like equations but: flip the inequality sign when multiplying or dividing by a negative number.

2x + 3 > 11 → 2x > 8 → x > 4

Graph on a number line: open circle for >/<, closed circle for ≥/≤.

Algebraic Word Problems

Translate words into equations:

• "3 more than twice a number" → 2n + 3
• "the product of x and 5 is 30" → 5x = 30 → x = 6
• Age problems: if Sam is 3 years older than Kim, and Kim is x, Sam is x + 3