Pelajaran Aljabar: Cara Menyelesaikan Soal Aljabar

Setiap soal aljabar bermuara pada beberapa langkah: sederhanakan, lakukan hal yang sama di kedua ruas, lalu periksa. Pelajaran ini mengajarkan setiap langkah dengan contoh soal yang jawabannya diperiksa oleh mesin matematika Sumzo.

18 artikel

5 menit membaca
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.
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Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
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Quadratic equations: how to solve them
Factorising, completing the square, the quadratic formula and the discriminant — and how to tell which method to use.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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 soal aljabar apa pun

Baca apa yang diminta: menyederhanakan bentuk aljabar, atau menyelesaikan persamaan untuk suatu huruf?
Sederhanakan setiap ruas: buka kurung dan gabungkan suku sejenis.
Batalkan operasi dalam urutan terbalik — penjumlahan dan pengurangan dulu, lalu perkalian dan pembagian — dengan melakukan hal yang sama di kedua ruas.
Periksa dengan memasukkan jawabanmu ke soal awal.

Contoh soal aljabar

Selesaikan $4(x - 2) = 2x + 6$ . Buka kurung: $4x - 8 = 2x + 6$ . Kurangi $2x$ : $2x - 8 = 6$ . Tambah 8: $2x = 14$ , jadi $x = 7$ .

Periksa: $4(7 - 2) = 20$ dan $2(7) + 6 = 20$ . Kedua ruas sama, jadi $x = 7$ benar.

Pelajaran aljabar mana yang saya butuhkan?

Persamaan dengan satu variabel: mulailah dengan persamaan dan persamaan linear.
Ada $x^2$ di soal: persamaan kuadrat, lalu pemfaktoran polinomial.
Pecahan yang memuat $x$ : bentuk rasional dan persamaan rasional.
Grafik, $f(x)$ , dan $y =$ : menggambar grafik persamaan, fungsi, dan gradien.
Cerita, bukan simbol: cara menyelesaikan soal cerita.

Pertanyaan umum

Di mana saya bisa mendapat bantuan aljabar untuk soal saya sendiri?

Ketik soalnya di kalkulator aljabar Sumzo: kalkulator ini menampilkan setiap langkah, dan mesin matematikanya memeriksa jawabannya. Pelajaran di sini mengajarkan metode di balik langkah-langkah itu.

Bagaimana cara memeriksa jawaban aljabar saya?

Masukkan jawabanmu ke persamaan awal. Jika kedua ruas hasilnya sama, jawabanmu benar — jika tidak, cari baris pertama tempat pengerjaanmu mengubah persamaan.

Apa yang harus saya pelajari dulu dalam aljabar?

Menyederhanakan bentuk aljabar dan menyelesaikan persamaan satu dan dua langkah. Semua yang berikutnya — persamaan kuadrat, fungsi, sistem persamaan — dibangun di atasnya.