Aulas de álgebra: como resolver um problema de álgebra

Todo problema de álgebra se resume a poucos movimentos: simplificar, fazer a mesma coisa dos dois lados e verificar. Estas aulas ensinam cada movimento com exemplos resolvidos cujas respostas são verificadas pelo motor matemático do Sumzo.

18 artigos

5 min de leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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 leitura
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.

Como abordar qualquer problema de álgebra

Leia o que está sendo pedido: simplificar uma expressão ou resolver uma equação para uma letra?
Simplifique cada lado: elimine os parênteses e junte os termos semelhantes.
Desfaça as operações na ordem inversa — primeiro adição e subtração, depois multiplicação e divisão — fazendo o mesmo dos dois lados.
Verifique substituindo sua resposta no problema original.

Um problema de álgebra resolvido

Resolva $4(x - 2) = 2x + 6$ . Expanda: $4x - 8 = 2x + 6$ . Subtraia $2x$ : $2x - 8 = 6$ . Some 8: $2x = 14$ , então $x = 7$ .

Verificação: $4(7 - 2) = 20$ e $2(7) + 6 = 20$ . Os dois lados são iguais, então $x = 7$ está certo.

De qual aula de álgebra eu preciso?

Equações com uma incógnita: comece por equações e equações lineares.
Um $x^2$ no problema: equações quadráticas e depois fatoração de polinômios.
Frações com $x$ : expressões racionais e equações racionais.
Gráficos, $f(x)$ e $y =$ : gráficos de equações, funções e inclinação.
Uma história em vez de símbolos: como resolver problemas com enunciado.

Perguntas frequentes

Onde consigo ajuda de álgebra com meu próprio problema?

Digite-o na calculadora de álgebra do Sumzo: ela mostra cada passo, e o motor matemático verifica a resposta. As aulas daqui ensinam os métodos por trás desses passos.

Como verifico minhas respostas de álgebra?

Substitua sua resposta na equação original. Se os dois lados derem o mesmo valor, está correta — se não, encontre a primeira linha em que sua resolução mudou a equação.

O que devo aprender primeiro em álgebra?

Simplificar expressões e resolver equações de um e dois passos. Tudo o que vem depois — quadráticas, funções, sistemas — se baseia nisso.