What algebra is (in plain English)
Algebra lets you use a letter (a variable) when a number is missing or changes. Your job is usually the same: keep the equation balanced while you “undo” operations until the variable is alone on one side.
Words you will see on day one
- Variable: A symbol (often x) standing in for an unknown value.
- Coefficient: The number parked next to a variable (in 4x, the coefficient is 4).
- Constant: A number without a variable, like -3 in 2x − 3.
- Expression: A math phrase without an equals sign (you simplify it).
- Equation: Two expressions with an equals sign (you solve it).
Solving one- and two-step equations
Think “inverse operations.” If something is added, subtract it from both sides. If something is multiplied, divide both sides. If the variable is trapped inside parentheses, you may distribute first or work from the inside out—whichever your teacher models for that problem type.
Always show a quick check when you can: substitute your answer back in and confirm both sides match.
Linear equations and graphs
A linear relationship graphs as a straight line. Slope-intercept form y = mx + b is the fastest way to read a line: m is slope (steepness + direction) and b is where the line crosses the y-axis.
Slope from two points: “rise over run.” Parallel lines share a slope; perpendicular lines have slopes that multiply to -1 (except vertical/horizontal pairs—ask your class for the shortcut your textbook uses).
Systems of equations (two unknowns)
A system is two equations that must be true at the same time. A solution is an (x, y) pair that makes both equations work. Common classroom tools:
- Graphing: The intersection point (if it exists) is the solution.
- Substitution: Solve one equation for a variable, plug into the other.
- Elimination (linear combination): Add or subtract equations so one variable cancels.
Intro to quadratics
A quadratic has an x² term. The standard form is ax² + bx + c = 0 (with a ≠ 0). You might factor, complete the square, or use the quadratic formula—your teacher will tell you which tool is required on a given assessment.
Quick meaning check: the discriminant (b² − 4ac) hints at how many real solutions you should expect; tie that idea back to the graph (where the parabola meets the x-axis).
Polynomials (like algebra’s LEGO)
A polynomial adds terms with whole-number exponents. “Combine like terms” means only merge pieces with the same variable and exponent. The degree is the largest exponent—use it to predict end behavior on graphs when your unit introduces that idea.
Quick review checklist
Run this on paper the night before an assessment—short answers, no peeking.
- Vocabulary: Five terms, defined in your own words.
- One strong example: Problem, diagram, quote+context, or map label your rubric would accept.
- Classic trap: What mistake shows up on every test—and what rule stops it?
- Connection: One sentence linking this topic to another unit from the same course.