🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{85-7x}{5}$$. 2. **Formula and rules:** When dividing a subtraction by a number, you can split the division over each term:

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **Problem statement:** We are given three functions: - $f_b(x) = (x-b)^2$

1. **Énoncé du problème :** Trouver la solution de l'équation $$x^2 + 3x - 2 = 2x + 4$$ parmi les choix proposés : A. 4, B. -2, C. 1, D. -3. 2. **Formule et règles importantes :**

1. **Solve by graphing: $x^2 - 7x + 12 = 0$** - The equation is quadratic and can be written as $y = x^2 - 7x + 12$.

1. **Énoncé du problème :** On modélise une façade du Parthénon par un rectangle GREC avec les longueurs :

1. Il problema chiede di risolvere il sistema di equazioni: $$\begin{cases} 2x + 3y - 3 = 0 \\ 3x - 2y + 2 = 0 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{x}{\sqrt[3]{xy^{2}}}$$. 2. **Recall the formula and rules:** The cube root of a product can be written as the product of c

1. **State the problem:** Simplify the expression $$\frac{x}{\sqrt[3]{xy^{2}}}$$. 2. **Recall the formula and rules:** The cube root of a product can be written as the product of c

1. **Énoncé du problème :** On considère la suite $(u_n)$ définie par $u_0=0$ et la relation de récurrence $$u_{n+1} = \frac{2u_n + 3}{u_n + 4}$$ pour tout entier naturel $n$.

1. Het probleem: We onderzoeken de eigenschappen van uitdrukkingen met de macht $x^3$. 2. Formule en regels: De macht $x^3$ betekent $x \times x \times x$.

1. **State the problem:** Simplify the expression $ (2x)^2 \times x $. 2. **Recall the formula:** When raising a product to a power, use the rule $ (ab)^n = a^n b^n $. Also, when m

1. Il problema riguarda le frazioni algebriche, cioè espressioni che contengono polinomi al numeratore e al denominatore. 2. La regola principale è che il denominatore non può mai

1. **Problema:** Si vuole costruire un recinto ad angolo formato da due lati maggiori di lunghezza $x$ e due lati minori congruenti, usando 60 m di rete. 2. **Formula per il perime

1. **Problème :** Factoriser l'expression $4x^2 - 28x + x^3 - 32$. 2. **Formule et méthode :** On regroupe les termes pour faciliter la factorisation par regroupement.

1. Das Problem lautet: Löse die Gleichung $$3x + 5 = 20$$ nach $$x$$ auf. 2. Die verwendete Formel ist die lineare Gleichung in der Form $$ax + b = c$$, wobei $$a$$, $$b$$ und $$c$

1. The problem is to plot the graph of the line given by the equation $$y = 4x + 3$$ where the gradient (slope) is positive. 2. The equation of a straight line in slope-intercept f

1. **State the problem:** We need to draw and understand the graph of the line given by the equation $y = 4x - 4$. 2. **Recall the formula:** The equation of a straight line in slo

1. **Problem statement:** Solve the system of equations using the Gleichsetzungsverfahren (equalization method) for part (a): (I) $4x + 5y = 12$

1. **State the problem:** Solve the equation $$\frac{x}{x - 1} = \frac{10}{x + 3}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, cross-multiply to eliminat

1. **Enunciado do problema:** Escreva na forma de polinómio reduzido cada uma das expressões dadas. 2. **Fórmula usada:** Para multiplicar dois polinómios, usamos a distributiva: $