🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $$2x^2 - \frac{8}{4x} = 3x^2 + \frac{6x}{2x}.$$\n\n2. **Rewrite the equation clearly:** $$2x^2 - \frac{8}{4x} = 3x^2 + \frac

1. **State the problem:** We are given the function $f(x) = 2x - 1$ and asked to analyze it from point $A$ to point $B$. 2. **Formula and rules:** This is a linear function of the

1. **Problem statement:** Solve the equation $$1 - \frac{y + 5}{3} = \frac{3(y - 1)}{4}$$ for $y$. 2. **Formula and rules:** To solve linear equations with fractions, first elimina

1. Masalah yang diberikan adalah fungsi implisit $$x^4 - 3xy^3 - 6xy^5 - 4 = 0$$. Kita diminta untuk memahami atau menyelesaikan fungsi ini. 2. Fungsi implisit adalah fungsi yang t

1. **Stating the problem:** We want to factor a common binomial, which means expressing it as a product of simpler expressions. 2. **Formula and rules:** When factoring a binomial,

1. Let's clarify what variables are in math problems. 2. Variables are symbols (like $x$, $y$) that represent unknown values.

1. The problem asks to find the total number of items delivered when a coach orders $4m$ boxes, each containing $2y+7$ items. 2. The expression to find the total items is given by

1. **Problem Statement:** Factoring by grouping is a method used to factor polynomials with four or more terms by grouping terms with common factors.

1. **State the problem:** Simplify the expression $$(3x - 2y + 4) + (x + y) + (2x - 3y)$$. 2. **Write down the expression:**

1. **Stating the problem:** We want to understand and work with trinomials of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants and $a \neq 0$. 2. **Formula and expla

1. **State the problem:** We need to find the 12th term of the harmonic sequence given by the terms 6, 4, 3. 2. **Recall the definition of a harmonic sequence:** A harmonic sequenc

1. **Problem Statement:** We want to understand how to factor trinomials of the form $x^2 + bx + c$. 2. **Formula and Rules:** A trinomial $x^2 + bx + c$ can be factored into two b

1. **State the problem:** We need to find the value of $k$ such that the numbers $6k-2$, $2k+7$, and $8k-4$ form an arithmetic progression (AP). 2. **Recall the AP property:** In a

1. **Stating the problem:** We want to find the greatest common monomial factor (GCMF) of given monomials. The GCMF is the largest monomial that divides each of the given monomials

1. Дана задача с тремя выражениями с модулями: $$A = |x^2 - 1| - |-x^2 - 4|$$

1. **State the problem:** Solve the equation $$\frac{2x + 3}{4} + 2 = 7$$ for $x$. 2. **Isolate the fraction:** Subtract 2 from both sides:

1. **State the problem:** Solve the equation $\left(2x + \frac{3}{4}\right) + 2 = 7$ for $x$. 2. **Write the equation clearly:**

1. Diketahui tiga suku pertama deret geometri adalah $x - 1$, $x - \frac{3}{2}$, dan $x - \frac{7}{4}$. Kita diminta mencari jumlah tak hingga deret tersebut. 2. Rumus jumlah tak h

1. Diketahui persamaan $$2^w \cdot a^x \cdot b^y \cdot c^z = 2013$$ dengan $a,b,c,x,y,z$ bilangan bulat positif, $w$ bilangan bulat nonnegatif, dan $a < b < c$. Kita diminta mencar

1. **Stating the problem:** We are given several fractions and mixed numbers representing lengths and heights, and a relation $m \frac{6}{8} = \frac{5}{2}$. We want to understand h

1. The problem is to add the fractions $\frac{6}{11}$ and $\frac{3}{5}$.\n\n2. To add fractions, we need a common denominator. The denominators here are 11 and 5.\n\n3. The least c