🧮 algebra

1. The first equation is $\frac{m - 3}{4} = \frac{m + 1}{3}$. We are given the LCD is 12. 2. Multiply both sides by 12 to clear the denominators:

1. The problem is to understand and evaluate \(\log_e\), which is the logarithm base \(e\) (known as the natural logarithm).\n\n2. The notation \(\log_e x\) is commonly written as

1. We are given the inequality $6 \leq -3(4-2x) < 8$ and need to solve for $x$. 2. Start by distributing $-3$ inside the parenthesis:

1. Enunciado del problema: Resolver la expresión $$\frac{\left(\frac{3}{1.2} + \sqrt{\frac{11}{25} + 1}\right) \div \left(-\frac{1}{2}\right) \cdot 3 \cdot \frac{2}{6}}{\frac{1}{5}

1. We are solving the equation: $$\frac{1}{2}(x + 6) = 4(x - 2)$$ 2. Start by distributing the terms on both sides:

1. **State the problem:** Simplify and analyze the expression $(a + 3\sqrt{5})^2 + a - b\sqrt{5} - 51$ and compare it to the expanded forms given. 2. **Expand the square:**

1. **State the problem:** Evaluate the function $f(x) = x^3 - 9x^2 + 24x - 18$ at $x = -1$ and analyze its properties. 2. **Calculate $f(-1)$:**

1. **Évaluer l'expression** $((\sqrt{2024} - 13)^0 - 2)^{2023}$ On sait que toute expression élevée à la puissance 0 vaut 1, sauf si la base est 0.

1. Stating the problem: We want to decompose the rational expression \(\frac{x+3}{(x-2)^2}\) into partial fractions. 2. Since the denominator is \((x-2)^2\), the partial fraction d

1. **Problem:** Lösen Sie die Gleichung $$\frac{1}{a} = \frac{1}{b} + \frac{1}{c}$$ nach $$a$$ auf. 2. Zuerst bringen wir die rechte Seite auf einen gemeinsamen Nenner:

1. The problem is to simplify or resolve the expression $x+\frac{3}{(x-2)^2}$.\n\n2. Since the terms are not combined under a single denominator, rewrite the expression with a comm

1. Problem statement: Analyze the function $f(x) = x^3 - 9x^2 + 24x - 18$ in terms of domain, range, intercepts, limits, derivatives, and continuity.\n\n2. Domain: Since $f(x)$ is

1. The problem is to find the domain of the function $$f(x) = \frac{1}{\sqrt{2x-4}}$$. 2. Start by identifying the domain restrictions. Since the denominator is a square root, the

1. The problem is to solve for $x$ given the equation $2x + 3 = 7$. 2. Start by isolating $x$ on one side of the equation. Subtract 3 from both sides:

1. Let's state the problem: Given the exercise number 1 as an example, we need to show how to solve it. 2. Since the problem details are not provided, let's assume a basic example

1) Calculer : 1. Calcul de A = $(-\sqrt{25})^2$\: \rightarrow -\sqrt{25} = -5$ donc $A = (-5)^2 = 25$.

1. Stating the problem: We want to decompose the rational expression $$\frac{x+3}{(x-2)^2}$$ into partial fractions. 2. Because the denominator has a repeated linear factor $(x-2)^

1. **State the problem:** We need to analyze the inequality $y \leq x + 2$. 2. **Rewrite the inequality:** It says that the value of $y$ is less than or equal to the value of the e

1. El problema consiste en realizar varias operaciones de división y multiplicación con números en notación científica. 2. Recordemos la regla básica para dividir potencias con bas

1. Given the expression to decompose: $$x + \frac{3}{(x - 2)^2}$$ 2. Since the denominator is $(x - 2)^2$, consider partial fractions of the form: $$\frac{A}{x - 2} + \frac{B}{(x -

1. The problem is to graph the linear inequality $y > 1$. 2. This inequality means we want all points where the $y$-coordinate is greater than 1.