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Algebra
Algebra turns a sentence about an unknown into an equation and then takes that equation apart, one legal move at a time, until the unknown stands alone. Every solution here shows the moves and graphs what they mean.
レッスン
Introductory
Linear equations
Isolate the unknown by doing the same thing to both sides.
2x + 3 = 7
Core
Quadratic equations
Factoring, the discriminant and the quadratic formula.
x^2 - 5x + 6 = 0
Core
Systems of equations
Substitution and elimination, and what the intersecting lines mean.
x + y = 3, x - y = 1
Core
Inequalities
Critical points, sign tests and interval notation.
x^2 - 4 > 0
Core
Factoring
Common factors, difference of squares, trinomials and cubes.
factor x^2 - 9
Introductory
Expanding
Distributing products and collecting like terms.
expand (x+1)^3
Core
Simplifying expressions
Cancelling common factors and combining fractions.
simplify (x^2-1)/(x-1)
Core
Functions and graphs
Zeros, slope, symmetry — reading a graph from its formula.
y = x^2 - 3
Advanced
Exponential and logarithmic equations
Undo an exponential with a logarithm, and a logarithm with an exponential.
2^x = 8
Advanced
Polynomial equations
Rational roots, factoring by division and the fundamental theorem of algebra.
x^3 - 6x^2 + 11x - 6 = 0
Core
Absolute value
Split into two cases and check each.
|x - 2| = 5
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