🧮 algebra

1. **State the problem:** Solve for $X$ in the equation:

1. Planteamos el problema: Resolver la ecuación $$\frac{x - ab}{a + b} + \frac{x - bc}{b + c} + \frac{x - ca}{c + a} = a + b + c$$ para $x$, con $a,b,c \in \mathbb{R}^+$.\n\n2. Par

1. Masalah: Contoh soal ini adalah menyelesaikan persamaan kuadrat $x^2 - 5x + 6 = 0$. 2. Rumus yang digunakan adalah rumus kuadrat: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ di m

1. We onderzoeken het aantal oplossingen van het stelsel zonder het expliciet op te lossen. 2. Voor een stelsel van twee lineaire vergelijkingen in twee onbekenden geldt:

1. Задача: Найти значение функции $$y$$ для заданного кусочно-заданного выражения: $$y=\begin{cases}2x, & \text{если } x < -2 \\ 3x + 2, & \text{если } x \geq -2\end{cases}$$

1. The problem is to find the solution for variables $a$ and $b$ given an equation or system involving them. 2. Since the problem statement is vague, let's assume a simple linear s

1. **Problema:** "FAMMI LE SCOMPOSIZIONI". 2. Per aiutarti a scomporre un'espressione, di solito si usa una di queste idee: raccoglimento, prodotti notevoli, trinomio speciale, dif

1. **Stato il problema.** La prima richiesta è: **indicare e motivare quali divisioni fra polinomi possono essere svolte**.

1. **State the problem:** Simplify the expression $$3\cdot\left(\frac{1}{2} + \frac{1}{3} - \frac{1}{6}\right) - 7\cdot\left(\frac{1}{4} + \frac{3}{4} - \frac{1}{8}\right) = \left(

1. **State the problem:** An item costs 500. The original selling price is 650. Later, 200 was added to the original selling price, and it was later tagged to sell at 630.

1. **State the problem:** Simplify the expression where $25 + x$ is the numerator of the second fraction. 2. **Identify the expression:** Suppose the expression is \( \frac{a}{b} +

1. **State the problem:** Solve the equation $$\frac{x}{2} = 25 + \frac{x}{12}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, first eliminate the denominat

1. **State the problem:** Simplify the expression $$\log_2 6 \cdot \log_3 6 - (\log_3 3 + \log_3 2)$$. 2. **Recall logarithm properties:**

1. **State the problem:** Simplify the expression $$\log_2 6 \cdot \log_3 6 - (\log_3 3 + \log_3 2)$$. 2. **Recall logarithm properties:**

1. **State the problem:** We have a straight line with gradient (slope) 1 that cuts the y-axis at (0, 7). This line is tangent to the circle defined by the equation $$x^2 + (y - 3)

1. **State the problem:** Simplify the expression $$-3\sqrt{7r^3} \cdot 6\sqrt{7r^2}$$. 2. **Recall the formula:** The product of square roots is the square root of the product: $$

1. **State the problem:** Kimi and Jarjit deposited money in two banks, Bank ABC and Bank PQR. We know the amounts deposited and the total interest each received after one year. We

1. **Stating the problem:** (a) Given matrix $$H=\begin{pmatrix}2 & 6 \\ 1 & k\end{pmatrix}$$, find the value of $$k$$ such that the inverse of $$H$$ does not exist.

1. **State the problem:** Fran's parking lot is rectangular. The length is 20 m less than the width. The perimeter is at least 160 m. We need to find the minimum width.

1. The problem is to understand and analyze the given polynomial expressions: $x^3 - 3x + 4$, $4x^2 - 2y + 7$, and $-x^2 + 5x - 2$. 2. These are polynomial expressions in variables

1. **State the problem:** Given the equation $$4\sqrt{2x} = 16$$, find the value of $$6x$$. 2. **Write the formula and rules:** We need to isolate $$x$$ by solving the equation. Re