🧮 algebra

1. **State the problem:** Simplify and solve the equation $ (x + 1)(x + 4) + 3(x - 2)(x - 1) = 4x(x - 6) $. 2. **Use the distributive property (FOIL) to expand each product:**

1. **Stating the problem:** Solve the given algebraic and coordinate geometry problems involving quadratic and quartic equations, inequalities, and systems of linear equations. 2.

1. Énonçons le problème : Montrer que $$U_{n+1} - U_n = \frac{-2}{n(n+1)(n+2)}$$ où $$U_n = \frac{1}{n(n+1)}$$. 2. Écrivons $$U_{n+1}$$ en remplaçant $$n$$ par $$n+1$$ dans $$U_n$$

1. **State the problem:** Solve the equation $5x - 3 [ x - (2x - 1)] = 3$ for $x$. 2. **Apply the distributive property inside the brackets:** First simplify the expression inside

1. **Résoudre l'équation** $\frac{4}{x-3} + \frac{5}{x+1} = 0$ et l'équation $(3x - 2)(4x + 1) = 2x(6x - 4)$. Pour la première équation, on cherche un dénominateur commun et on rés

1. Énonçons le problème : Montrer que $$U_{n+1} - U_n = \frac{-2}{n(n+1)(n+2)}$$. 2. Pour cela, supposons que la suite $U_n$ est définie par une expression permettant de calculer $

1. **State the problem:** Simplify and solve the equation $8 (x - 2) - 5 (3 - x) + 16 = 15 - 4 (3 - x)$. 2. **Apply the distributive property:** Multiply each term inside the paren

1. **State the problem:** Solve the equation $12x - 3(x - 2) = 3(x + 4)$ for $x$. 2. **Apply the distributive property:** Expand the terms with parentheses.

1. **State the problem:** Solve the equation $ (x + 5)(x + 1) + 2(x - 4)(x + 3) = 3x(x + 8) $.\n\n2. **Expand each product:**\n\n$ (x + 5)(x + 1) = x^2 + x + 5x + 5 = x^2 + 6x + 5

1. **State the problem:** Solve the equation $2x - 7 [ x - (3x + 2)] = 9$ for $x$. 2. **Apply the distributive property inside the brackets:**

1. **State the problem:** Simplify and solve the equation $3 (x - 3) - 5 (3 - x) + 12 = 15 - 3 (3 - x)$. 2. **Distribute the terms:** Apply the distributive property to remove pare

1. **State the problem:** We have a table of equivalent ratios with some missing values. The table is: | ? | 14 |

1. **بيان المسألة:** لدينا قطعة أرض مستطيلة الشكل طولها يزيد عن عرضها ب 50 مترًا، ومحيطها 420 مترًا.

1. نبدأ بحل التمرين الأول A: المطلوب هو حساب

1. The problem asks which system of inequalities has no solution set. 2. A system of inequalities has no solution if the inequalities contradict each other, meaning there is no ove

1. **State the problem:** We need to find which pair $(x,y)$ satisfies the system of inequalities: $$x - 2y < 5$$

1. Stating the problem: Simplify the expression $\sqrt{x}5$. 2. Understanding the expression: The expression $\sqrt{x}5$ means $5$ multiplied by the square root of $x$, which can b

1. **State the problem:** We have 2000 people attending the first webinar. 2. **Given data:**

1. **State the problem:** We have the function $g(x) = \frac{1}{11}(6 \cdot 2^x + 7)$ and want to find the greatest constant $k$ such that $g(x) > k$ for all $x$. 2. **Analyze the

1. **State the problem:** A man and his apprentice paint a room. The man takes 1 hour less than the apprentice to paint alone. Together, they take 72 minutes to paint the room. Fin

1. **State the problem:** Solve the equation $5x - 15 = 15$ for $x$. 2. **Write down the equation:**