Lecciones de álgebra: cómo resolver un problema de álgebra

Todo problema de álgebra se reduce a unos pocos pasos: simplificar, hacer lo mismo en ambos lados y comprobar. Estas lecciones de álgebra enseñan cada paso con ejemplos resueltos cuyas respuestas comprueba el motor matemático de Sumzo.

18 artículos

5 min de lectura
Equations: what they are and how to solve them
What an equation is, what its solution means, and how to solve equations step by step — from one-step equations to fractions and two variables.
1 min de lectura
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
2 min de lectura
Quadratic equations: how to solve them
Factorising, completing the square, the quadratic formula and the discriminant — and how to tell which method to use.
1 min de lectura
Slope and the equation of a line
What slope measures, how to find it from two points, and how to write a line as y = mx + b.
4 min de lectura
How to simplify radicals (simplest radical form)
How to simplify radicals by taking out perfect-square factors, what simplest radical form means, and how to simplify radical expressions — with checked examples.
2 min de lectura
Rational equations: how to solve them
What a rational equation is, how to solve rational equations by multiplying by the lowest common denominator, and why every answer must be checked.
3 min de lectura
Factoring polynomials: a step-by-step guide
The steps for factoring polynomials — common factor first, then two, three or four terms — with worked examples, each checked by multiplying back out.
3 min de lectura
Solving inequalities: how to solve and graph them
Solving inequalities like equations — with one extra rule — and showing the answer on a number line, in interval notation and as a shaded region.
2 min de lectura
What is a solution in math? Examples with one, none or many
A solution is a value that makes an equation true. How to check one, and examples with one solution, no solution, all real numbers and two solutions.
2 min de lectura
How to solve a word problem: 5 steps that work
A five-step method for solving word problems, the key words that turn into maths, and worked examples — ages, consecutive numbers, discounts and tickets.
2 min de lectura
How to graph an equation: lines, parabolas and more
Three ways to graph an equation — a table of values, slope and intercept, and key points of a parabola — with worked examples and how to match a graph to its equation.
3 min de lectura
Functions: how to graph a function, domain, range and f(g(x))
Function notation, how to graph a function from its formula, how to find its domain and range, and how composite functions such as f(g(x)) work.
2 min de lectura
Polynomials: how to simplify, expand and solve them
What a polynomial is, how to simplify and expand polynomials, and how to solve polynomial equations by factoring — with checked examples.
2 min de lectura
Rational expressions: simplify, multiply, divide, add and subtract
What rational expressions are, their excluded values, and how to simplify, multiply, divide, add and subtract them — then solve rational equations.
2 min de lectura
How to solve literal equations (rearranging formulas)
A literal equation has several letters. Solving it means isolating one of them — the same moves as an ordinary equation, with letters instead of numbers.
1 min de lectura
How to simplify expressions and complex fractions
How to simplify the following kinds of expression: like terms, brackets, exponents and complex fractions (a fraction inside a fraction), each with checked examples.
1 min de lectura
Find x: how to solve for x in equations, angles and triangles
The questions that say “find x” — equations, angles on a line, triangle angles, Pythagoras and similar shapes — and the one idea behind all of them.
2 min de lectura
Systems of equations and graphing systems of linear inequalities
How to find the solution to a system of equations three ways, then how to graph a system of inequalities: boundary lines, shading and the overlap.

Cómo abordar cualquier problema de álgebra

Lee qué se pide: ¿simplificar una expresión o resolver una ecuación para una letra?
Simplifica cada lado: quita los paréntesis y agrupa los términos semejantes.
Deshaz las operaciones en orden inverso — primero sumas y restas, luego multiplicaciones y divisiones — haciendo lo mismo en ambos lados.
Comprueba sustituyendo tu respuesta en el problema original.

Un problema de álgebra resuelto

Resuelve $4(x - 2) = 2x + 6$ . Desarrolla: $4x - 8 = 2x + 6$ . Resta $2x$ : $2x - 8 = 6$ . Suma 8: $2x = 14$ , así que $x = 7$ .

Comprobación: $4(7 - 2) = 20$ y $2(7) + 6 = 20$ . Ambos lados coinciden, así que $x = 7$ es correcto.

¿Qué lección de álgebra necesito?

Ecuaciones con una incógnita: empieza por ecuaciones y ecuaciones lineales.
Hay un $x^2$ en el problema: ecuaciones cuadráticas y luego factorización de polinomios.
Fracciones con $x$ : expresiones racionales y ecuaciones racionales.
Gráficas, $f(x)$ y $y =$ : graficar ecuaciones, funciones y pendiente.
Una historia en lugar de símbolos: cómo resolver problemas con enunciado.

Preguntas frecuentes

¿Dónde consigo ayuda de álgebra con mi propio problema?

Escríbelo en la calculadora de álgebra de Sumzo: muestra cada paso y su motor matemático comprueba la respuesta. Las lecciones de aquí enseñan los métodos detrás de esos pasos.

¿Cómo compruebo mis respuestas de álgebra?

Sustituye tu respuesta en la ecuación original. Si ambos lados dan lo mismo, es correcta; si no, busca la primera línea en la que tu desarrollo cambió la ecuación.

¿Qué debo aprender primero en álgebra?

Simplificar expresiones y resolver ecuaciones de uno y dos pasos. Todo lo posterior — cuadráticas, funciones, sistemas — se basa en eso.