🧮 algebra

1. **نص المشكلة:** حل المعادلة $$\frac{1}{x+2} + \frac{1}{x-2} = \frac{4}{(x+2)(x-2)}$$ مع ملاحظة أن هناك حلول غير مقبولة إذا جعلت المقامات صفرًا. 2. **صيغة الحل:** نستخدم قاعدة جم

1. **State the problem:** Solve the equation $7 = 2^x - 7 + 3$ for $x$. 2. **Simplify the equation:** Combine like terms on the right side.

1. The problem asks to match scenarios with the best graph based on given variables. 2. For each scenario, identify the variables and their relationship (distance/time, speed/time,

1. **Problem Statement:** We need to divide the given polynomials $f(x)$ by $g(x)$ for each part (a), (b), and (c). 2. **Formula and Rules:** Polynomial division is similar to long

1. **Stating the problem:** Solve the system of linear equations using Gaussian elimination: $$\begin{cases} x - 2y + 3z = 2 \\ 2x + y + z = 4 \\ 3x - y + 4z = 6 \end{cases}$$

1. Arazoa: Gauss-en formula erabiliz, zenbaki segida baten batura azkar kalkulatu behar dugu. 2. Gauss-en formula hau da: $$S_n = \frac{n(n+1)}{2}$$ non $S_n$ segidaren lehen $n$ z

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x - 2y + 3z = 2 \\ 2x + y + z = 4 \\ 3x - y + 4z = 6 \end{cases}$$

1. **State the problem:** Given the equation $$3 \log_3(2x - 1) = 2 + \log_3(14x - 25)$$, we need to show that it leads to the cubic equation $$2x^3 - 3x^2 - 30x + 56 = 0$$.

1. **State the problem:** We need to find the normal price of an umbrella given that its sale price after an 18% reduction is 25.83. 2. **Formula and explanation:** The sale price

1. **State the problem:** Solve the system of linear equations using Gaussian elimination: $$\begin{cases} x + y - 4z = 3 \\ x - y - 2z = 1 \\ 2x + y - 5z = 5 \end{cases}$$

1. **State the problem:** Vijay's wages increased from 115 to 130 per week. We need to find the percentage increase to one decimal place. 2. **Formula:** The percentage increase is

1. **State the problem:** Simplify the expression $6 \div 2(1+2)$. 2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication and division from le

1. Problem: Find the cost of 10 kg of tea leaves when 3 kg cost 18. Formula: Cost is directly proportional to weight, so $\frac{Cost_1}{Weight_1} = \frac{Cost_2}{Weight_2}$.

1. The user requests solutions for multiple exercises (3.1 to 3.5 and Review Exercise 3) from Unit 3, but no specific problems are provided. 2. To assist effectively, please provid

1. The problem is to find the equivalent decimal form of the fraction $\frac{1}{53}$.\n\n2. The formula to convert a fraction to a decimal is to divide the numerator by the denomin

1. **State the problem:** We need to multiply the binomials $(3x - 4)(3x + 3)$ using the FOIL method. 2. **Recall the FOIL method:** FOIL stands for First, Outer, Inner, Last. It i

1. **State the problem:** We need to factor the quadratic expression $2x^2 + x - 10$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. **Problem:** Calculate $\left(\frac{1}{2} + \frac{1}{3}\right) - \frac{2}{3}$. Formula: Add fractions by finding a common denominator.

1. **State the problem:** Factorize the expression $25x^2 - 5x + 30x^3$ by grouping. 2. **Recall the method:** Factorization by grouping involves grouping terms with common factors

1. **State the problem:** Solve the system of equations: $$xy + 4x + 8y = 1$$

1. **Stating the problem:** We need to solve the algebraic expression or equation provided by the user. Since no specific problem was given, please provide the problem statement fo