Algebra I quick reference
Notes and worked examples for the first four units.
1. Solving linear equations
The goal is to get the variable by itself. Keep the equation balanced by doing the same operation to both sides.
| 3x + 5 = 20 | Starting equation |
| 3x = 15 | Subtract 5 from both sides |
| x = 5 | Divide both sides by 3 |
Check the answer by replacing x with 5: 3(5) + 5 = 20. The left side equals the right side, so x = 5 is correct.
2. Slope and graphing
Slope tells how quickly a line rises or falls. Use two points on the line and divide the change in y by the change in x.
For the points (2, 3) and (6, 11), the rise is 8 and the run is 4. The slope is 8 ÷ 4 = 2.
| Slope | What the line does |
|---|---|
| Positive | Rises from left to right |
| Negative | Falls from left to right |
| Zero | Stays horizontal |
| Undefined | Stays vertical |
3. Systems of equations
A solution to a system must make both equations true. Elimination works well when adding the equations removes one variable.
| 2x + y = 7 | First equation |
| x − y = 2 | Second equation |
| 3x = 9 | Add the equations |
| x = 3 | Divide by 3 |
| y = 1 | Substitute x = 3 into either equation |
The solution is (3, 1). On a graph, this is the point where the two lines cross.
4. Exponent rules
Exponent rules apply when the bases match. A negative exponent means take the reciprocal. It does not make the value negative.
| Rule | Example |
|---|---|
| xa · xb = xa+b | x² · x³ = x⁵ |
| xa ÷ xb = xa−b | x⁷ ÷ x² = x⁵ |
| (xa)b = xab | (x²)³ = x⁶ |
| x⁰ = 1 | 12⁰ = 1 |
| x−a = 1 / xa | x−2 = 1 / x² |
Practice problem
Solve 2(3x − 1) = 16.