Lezioni di algebra: come risolvere un problema di algebra

Ogni problema di algebra si riduce a poche mosse: semplificare, fare la stessa cosa da entrambi i lati e verificare. Queste lezioni insegnano ogni mossa con esempi svolti le cui risposte sono verificate dal motore matematico di Sumzo.

18 articoli

5 min di lettura
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 di lettura
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
2 min di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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.

Come affrontare qualsiasi problema di algebra

Leggi cosa viene chiesto: semplificare un’espressione o risolvere un’equazione rispetto a una lettera?
Semplifica ogni membro: togli le parentesi e raccogli i termini simili.
Annulla le operazioni in ordine inverso — prima addizione e sottrazione, poi moltiplicazione e divisione — facendo lo stesso da entrambi i lati.
Verifica sostituendo la tua risposta nel problema originale.

Un problema di algebra svolto

Risolvi $4(x - 2) = 2x + 6$ . Sviluppa: $4x - 8 = 2x + 6$ . Sottrai $2x$ : $2x - 8 = 6$ . Aggiungi 8: $2x = 14$ , quindi $x = 7$ .

Verifica: $4(7 - 2) = 20$ e $2(7) + 6 = 20$ . I due membri coincidono, quindi $x = 7$ è corretto.

Di quale lezione di algebra ho bisogno?

Equazioni con un’incognita: inizia da equazioni ed equazioni di primo grado.
Un $x^2$ nel problema: equazioni di secondo grado, poi scomposizione dei polinomi.
Frazioni con $x$ : espressioni razionali ed equazioni fratte.
Grafici, $f(x)$ e $y =$ : grafici di equazioni, funzioni e pendenza.
Una storia invece dei simboli: come risolvere i problemi con testo.

Domande frequenti

Dove trovo aiuto in algebra per il mio problema?

Scrivilo nella calcolatrice di algebra di Sumzo: mostra ogni passaggio e il suo motore matematico verifica la risposta. Le lezioni qui insegnano i metodi dietro quei passaggi.

Come verifico le mie risposte di algebra?

Sostituisci la risposta nell’equazione originale. Se i due membri sono uguali è corretta — altrimenti cerca la prima riga in cui il tuo svolgimento ha cambiato l’equazione.

Cosa devo imparare per primo in algebra?

Semplificare espressioni e risolvere equazioni a uno e due passaggi. Tutto il resto — secondo grado, funzioni, sistemi — si basa su questo.