🧮 algebra

1. **Énoncé du problème :** Calculer les expressions données en respectant les priorités opératoires et simplifier les résultats sous forme de fractions. 2. **Rappel des règles imp

1. **Énoncé du problème :** Résoudre l'inéquation $x^2 - 3x + 2 > 0$. 2. **Formule et règle utilisée :** Pour résoudre une inéquation polynomiale du second degré, on commence par t

1. Das Problem: Wir sollen eine Gleichung oder ein Problem mit einer Formel lösen. Da keine konkrete Aufgabe gegeben ist, erkläre ich, wie man eine allgemeine Formel anwendet. 2. F

1. The problem asks how we know that $4^3 = 64$. 2. The expression $4^3$ means $4$ multiplied by itself 3 times: $4 \times 4 \times 4$.

1. The problem asks to find the cube root of 64, written as $\sqrt[3]{64}$.\n\n2. The cube root of a number $x$ is a value $y$ such that $y^3 = x$.\n\n3. We want to find $y$ such t

1. **State the problem:** Explain how to factor the expression $x^2 - 25$ into $(x - 5)(x + 5)$. 2. **Recall the difference of squares formula:** For any two terms $a$ and $b$, the

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Recall the division rule for fractions:** Dividing by a

1. **State the problem.** Find the limit $\lim_{x\to 3}\frac{x^2-9}{x-3}$.

1. **Problem:** Solve $a^3+a^2=36$ for $a$. 2. **Formula and idea:** First, move everything to one side:

1. **State the problem:** Solve the equation $$a^3 + a^2 = 36$$ for the variable $a$. 2. **Rewrite the equation:** We want to find $a$ such that $$a^3 + a^2 - 36 = 0$$.

1. The problem is to solve the quadratic equation $2x^2 - 4x - 6 = 0$. 2. The formula to solve quadratic equations is the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a

1. **State the problem:** Find the value of $x$ such that $f(x) = 4$ given the function $f(x) = 2x + 2$. 2. **Write the equation:**

1. **State the problem:** We need to find the equation of a line given its graph. 2. **Analyze the graph:** The line crosses the y-axis at $-2$ and the x-axis at $5$.

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **State the problem:** We are given two linear equations: $$2x + 3y = 7$$

1. **State the problem:** Evaluate the expression $$6 \div 2(1+2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **Problem:** Solve the system of equations $2x+y=8$ and $2x-y=12$, then find $x$ and $y$. 2. **Formula used:** For a system, we can use elimination by adding the equations to re

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**

1. **State the problem:** Add the two complex numbers $(12+3i)$ and $(14+8i)$. 2. **Formula used:** To add complex numbers, add their real parts and their imaginary parts separatel