🧮 algebra

1. **State the problem:** Solve the equation $5(5-7) - 2(3+4) = 0$. 2. **Apply the distributive property:** Multiply inside the parentheses by the numbers outside.

1. **State the problem:** Find the exact values of $x$ such that $$21\log_5(x + 5) - \log_5(2x + 2) = 2.$$\n\n2. **Recall the logarithm properties:**\n- $a\log_b(c) = \log_b(c^a)$\

1. The problem involves simplifying and understanding the expression related to the variables $a$, $b$, $c$, $r$, $B$, $D$, and $\Delta$ given in the form of fractions and products

1. **State the problem:** Simplify and solve the equation $$\frac{a+b}{a \times b} - \frac{a-b}{a \times b} = \frac{b}{8}$$ for $a$ and $b$. 2. **Identify the formula and rules:**

1. **State the problem:** Solve the quadratic equation $x^2 + 25x = 0$. 2. **Formula and rules:** To solve quadratic equations, one common method is factoring. If the equation can

1. **بيان المسألة:** لدينا متتالية حسابية أساسها $r = -5$، ومعلومة أن $u_3^2 + u_7^2 = 650$. المطلوب:

1. Let's state the problem: We want to understand how to work with expressions where the powers of $x$ are different, for example, one term has $x^3$ (cube) and another has $x^2$ (

1. The problem is to understand why the expression $5\left(\frac{3y}{5}\right)$ simplifies as it does. 2. The expression involves multiplication of a number by a fraction: $5 \time

1. The problem asks to draw the graph of the function $$y=3x+2x-7$$ and from that graph find the value of $$y=2x-1$$. 2. First, simplify the function $$y=3x+2x-7$$ by combining lik

1. **State the problem:** Solve the linear inequality $$4 - \frac{3y}{5} \leq 7$$. 2. **Isolate the term with the variable:** Subtract 4 from both sides:

1. نُعطى متتالية حسابية متزايدة $(u_n)$ حيث $u_3=2$ و $\frac{1}{u_5} - \frac{1}{u_1} = \frac{3}{8}$. 2. نعلم أن المتتالية الحسابية تحقق $u_n = u_1 + (n-1)r$ حيث $r$ هو الأساس.

1. نُعطى متتالية حسابية متزايدة \((u_n)\) حيث \(u_3 = 2\) و \[\frac{1}{u_5} - \frac{1}{u_1} = \frac{3}{5}\]

1. ปัญหาคือการแก้สมการ $2x + 3 = 11$ เพื่อหาค่า $x$. 2. สูตรที่ใช้คือการแก้สมการเชิงเส้นรูปแบบ $ax + b = c$ โดยการย้ายข้างและหารเพื่อหาค่า $x$.

1. **State the problem:** Solve the equation $$0 = -3x^5 - 10x^3 + 45x$$ for $x$. 2. **Identify the formula and rules:** This is a polynomial equation. To solve it, we factor the p

1. **State the problem:** Solve for $c$ in the equation $c + 11 = 77$. 2. **Formula and rules:** To isolate $c$, subtract 11 from both sides of the equation. This uses the subtract

1. **State the problem:** We need to find the value of $b$ given the equation $b + 53 = 121$. 2. **Formula and rules:** To solve for $b$, we use the rule of equality which states t

1. The first problem involves the function $f(x) = 2x^3 - 3x^2 - 36x$ and inequalities involving $x$. 2. We need to analyze the inequalities given: $x < 2$ or $x > 3$, $x < 2$ or $

Let's simplify the first problem step by step! 🎉 **Problem 1:** $\sqrt{327} + \sqrt{50} - \sqrt{7}$

1. The problem is to understand why the error occurred when trying to define or manipulate the expression $$E := 3 \cdot x \cdot y^3 - \tan(2 \cdot y) = 5(x^2 + 3x)^3 + 5y$$ and ho

1. **State the problem:** We have two shops selling the same laptop. Shop A sells it for 475 with a 16% discount. Shop B sells it with a 15% discount, and the total price after dis

1. **State the problem:** Simplify the expression $5a^2b + ab^2$ if possible. 2. **Identify common factors:** Both terms have a common factor of $ab$.