🧮 algebra

1. **Énoncé du problème :** Soit la fonction linéaire $f$ définie par $f(x) = -\frac{5}{2}x$.

1. **State the problem:** Expand and simplify the expression $$(4x - 3)(2x - 5)$$. 2. **Recall the distributive property (FOIL method):** To multiply two binomials, multiply each t

1. **State the problem:** Expand and simplify the expression $$5m (2m - 5n) - 3n (m + 2n)$$. 2. **Use the distributive property:** Multiply each term inside the brackets by the ter

1. **State the problem:** We have a sequence where the first term is $5x$ and each subsequent term is found by adding $2x + 3$ to the previous term. 2. **Formula and rule:** The te

1. **State the problem:** Solve the inequality $$\frac{2x - 3}{x + 5} \leq 0$$. 2. **Recall the rule for rational inequalities:** A rational expression $$\frac{A}{B} \leq 0$$ is le

1. The problem is to simplify or understand the expression $\frac{5\pi}{4} + 6m$. 2. This expression is a sum of two terms: a constant term $\frac{5\pi}{4}$ and a variable term $6m

1. **Problem statement:** A jar starts with 1000 g of sugar. Each day, half of the sugar present is removed. We want to find how much sugar remains after 5 days. 2. **Formula:** Th

1. The problem is to solve the equation or expression labeled as "B" (since the user specified "the B one, not the A"). 2. Since the user did not provide the explicit problem state

1. Planteamos el problema: Resolver la ecuación cuadrática $$3x^2 + 3x - 1 = 0$$ usando la fórmula general. 2. Recordemos la fórmula general para ecuaciones cuadráticas $$ax^2 + bx

1. Énoncé du problème : Résoudre dans $\mathbb{R}$ l'inéquation $$y(x) < -2x + 5.$$ 2. Pour résoudre une inéquation de la forme $$y(x) < f(x),$$ il faut trouver les valeurs de $x$

1. The problem asks: What is $c$? 2. To answer this, we need more context or an equation involving $c$.

1. Énoncé du problème : Résoudre dans $\mathbb{R}$ l'inéquation $$y(x) < -2x + 5$$. 2. Pour résoudre cette inéquation, il faut comprendre que $y(x)$ est une fonction dont on cherch

1. **Problem:** Solve the first pair of simultaneous equations: $$\frac{1}{2}x + \frac{2}{3}y = 6 \frac{1}{5}$$

1. **State the problem:** Simplify the expression $$\left(\frac{x^{\frac{4}{3}}}{-125 y^{-\frac{9}{3}} z^{\frac{8}{3}}}\right)^{-\frac{1}{3}}$$. 2. **Recall the power of a quotient

1. **State the problem:** Solve the equation $$\left(\frac{3}{7}\right)^{3x-7} = \left(\frac{7}{3}\right)^{7x-3}.$$\n\n2. **Rewrite the right side:** Note that $$\frac{7}{3} = \lef

1. **State the problem:** Simplify the expression $$\frac{(x + \sqrt{3})^2}{\sqrt{2} x^2 - 3\sqrt{2}} \cdot \frac{\sqrt{2}x - \sqrt{6}}{3}$$. 2. **Expand the numerator of the first

1. **Problem:** Factorize the expression $x^2 - x - 90$ using the AC method. 2. **Formula and rules:** The AC method involves multiplying the coefficient of $x^2$ (which is $1$) by

1. **State the problem:** We are given the function $f(x) = -x - 4$ and need to find the values of $f(x)$ for $x = -2, 4, 6, 4, 5$. 2. **Formula used:** The function is defined as

1. **State the problem:** Solve for $\alpha$ in the equation $$25 = 6\alpha + 7$$. 2. **Isolate the term with $\alpha$:** Subtract 7 from both sides:

1. **State the problem:** Find the domain and range of a function. Since the function is not specified, let's consider a general approach. 2. **Domain:** The domain of a function i

1. The problem is to analyze the function $f(x) = 1 + x^2$. 2. This is a quadratic function where the term $x^2$ dominates the shape.