🧮 algebra

1. We are asked to find the solution set of the inequality $$3 - \frac{1}{2x} \leq 1$$. 2. Start by isolating the term with $x$:

1. **Problem Statement:** Find the HCF of 408 and 1023 expressed in the form $1023x + 408y$ and determine the values of $x$ and $y$. 2. **Formula and Method:** The HCF (Highest Com

1. נניח שמספר התשלומים בהצעה I הוא $n$.\n2. סכום התשלומים בהצעה I הוא סכום סדרה חשבונית עם איבר ראשון $a_1=180$ והפרש $d=15$.\n3. סכום התשלומים בהצעה I הוא \n$$S_1 = \frac{n}{2} \t

1. **State the problem:** Solve the equation $2x(x-4) = (1-x)(x+2)$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $$\frac{2}{x} = 2x + 1$$ for $x$. 2. **Rewrite the equation:** To eliminate the fraction, multiply both sides by $x$ (assuming $x \neq

1. **State the problem:** We are given the function $f(x) = \sqrt{x}$ and asked to determine the reflection represented by the function $f(y) = \sqrt{-x}$. 2. **Recall the reflecti

1. **State the problem:** Simplify fully the expression $$\left(\frac{9t^4 w^9}{18t^6 w^{10}}\right)^{-2}$$. 2. **Recall the rules:**

1. The problem is to analyze the function $$f(x) = \frac{x^3 - 3 \sin x}{1 + \tan x}$$ and also consider the function $$f(x) = \sqrt{x}$$. 2. For the first function, we want to und

1. **State the problem:** Solve the equation $x(x-2)=26$ for $x$. 2. **Write the equation:**

1. **State the problem:** Solve the equation $X(x-4) = (3-x)(x+3)$ for $x$. 2. **Write down the equation:**

1. لنبدأ بحل السؤال الأول: \text{مدى الاقتران } f = |3س - 5|. 2. الاقتران المطلق \left| x \right| يعني أن الناتج دائمًا غير سالب، أي \geq 0.

1. **State the problem:** Simplify the expression $$(x-3)(x+3)$$. 2. **Formula used:** This is a product of conjugates, which follows the identity $$ (a-b)(a+b) = a^2 - b^2 $$.

1. السؤال: قيم س من تجعل منحنى الترانك في (س) حيث $س^4 + 1 > 0$؟ 2. نلاحظ أن $س^4$ هو عدد موجب أو صفر لأي قيمة حقيقية لـ $س$، و $1$ موجب دائماً.

1. **Problem statement:** Solve the equation $$(x - 1)^3 + 3(x + 1)^2 + x(x - 3)(x + 3) = 2x^3 + 2.$$ 2. **Recall formulas and rules:**

1. **Problem:** If $p-1$, $p+1$, and $2p+3$ are in arithmetic progression (A.P.), find the value of $p$. 2. **Formula:** In an A.P., the middle term is the average of the first and

1. نص المسألة: النص المرسل غير واضح ومشوش، ويحتاج إلى توضيح.

1. **تمرين 1 - الدالة و(x) = 3x^2 + 2 + x** - **المطلوب:**

1. نبدأ بحل التمرين 1، الدالة \( f(x) = 3x^2 + 2 + x \). 2. \textbf{مجموعة تعريف الدالة}: الدالة كثيرة حدود، معرفة لكل \( x \in \mathbb{R} \).

1. Define a sequence. A sequence is an ordered list of numbers following a particular pattern.

1. **Problem Statement:** We have the function $g(x) = 3x^2 + 2$ and a set of points for $f(x)$ given as:

1. **State the problem:** Simplify or analyze the expression $2\sin^3(x)(x^2-1)$. 2. **Understand the components:** The expression is a product of $2$, $\sin^3(x)$ (which means $\s