Pelajaran Algebra: Cara Menyelesaikan Masalah Algebra

Setiap masalah algebra bergantung pada beberapa langkah: permudahkan, lakukan perkara yang sama pada kedua-dua belah, dan semak. Pelajaran ini mengajar setiap langkah dengan contoh berjawapan yang jawapannya disemak oleh enjin matematik Sumzo.

18 artikel

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

Cara mendekati sebarang masalah algebra

Baca apa yang diminta: mempermudahkan ungkapan, atau menyelesaikan persamaan untuk satu huruf?
Permudahkan setiap belah: kembangkan kurungan dan kumpulkan sebutan serupa.
Buat semula operasi dalam susunan terbalik — tambah dan tolak dahulu, kemudian darab dan bahagi — dengan melakukan perkara yang sama pada kedua-dua belah.
Semak dengan menggantikan jawapan anda ke dalam masalah asal.

Contoh masalah algebra berjawapan

Selesaikan $4(x - 2) = 2x + 6$ . Kembangkan: $4x - 8 = 2x + 6$ . Tolak $2x$ : $2x - 8 = 6$ . Tambah 8: $2x = 14$ , maka $x = 7$ .

Semakan: $4(7 - 2) = 20$ dan $2(7) + 6 = 20$ . Kedua-dua belah sama, maka $x = 7$ betul.

Pelajaran algebra mana yang saya perlukan?

Persamaan dengan satu anu: mulakan dengan persamaan dan persamaan linear.
Ada $x^2$ dalam masalah: persamaan kuadratik, kemudian pemfaktoran polinomial.
Pecahan yang mengandungi $x$ : ungkapan nisbah dan persamaan nisbah.
Graf, $f(x)$ dan $y =$ : melukis graf persamaan, fungsi dan kecerunan.
Cerita, bukan simbol: cara menyelesaikan soalan berayat.

Soalan lazim

Di mana saya boleh dapatkan bantuan algebra untuk masalah saya sendiri?

Taipkannya dalam kalkulator algebra Sumzo: ia menunjukkan setiap langkah, dan enjin matematiknya menyemak jawapan. Pelajaran di sini mengajar kaedah di sebalik langkah-langkah itu.

Bagaimana saya menyemak jawapan algebra saya?

Gantikan jawapan anda ke dalam persamaan asal. Jika kedua-dua belah sama, jawapan itu betul — jika tidak, cari baris pertama di mana jalan kerja anda mengubah persamaan.

Apa yang patut saya pelajari dahulu dalam algebra?

Mempermudahkan ungkapan dan menyelesaikan persamaan satu dan dua langkah. Semua yang seterusnya — kuadratik, fungsi, sistem persamaan — dibina di atasnya.