🧮 algebra

1. **State the problem:** Solve the equation $$\frac{x - 1}{2} + 3x = 10$$. 2. **Formula and rules:** To solve linear equations, combine like terms and isolate the variable on one

1. The problem is to write the equation $2y + 5 = 0$ in normal form. 2. The normal form of a linear equation in one variable is to isolate the variable on one side.

1. **Problem:** Find $k$ if $f(x) = 3x^4 - 2x^3 + kx + 7$ is divisible by $x+1$. 2. **Formula:** If $x+1$ is a factor, then $f(-1) = 0$ (Factor Theorem).

Let's solve the function step by step! 🎉 **Step 1:** Understand the function $f(x) = \log(x^2 - 4)(x^2 - x)$.

1. **State the problem:** We need to find the nature of the roots of the quadratic equation $x^2 + 5x - 6 = 0$ using the discriminant. 2. **Recall the quadratic equation and discri

1. مسئله: حل معادله $$\frac{2x+4}{5} = \frac{7x+3}{3}$$. 2. فرمول: برای حل معادله کسرها، ابتدا دو طرف را در مخرج مشترک ضرب می‌کنیم تا کسرها حذف شوند.

1. Stating the problem: We have the function $$y = \frac{4}{-x - 2} - 4$$ and need to find: 1.1 The domain of the function.

1. **State the problem:** Calculate the value of the expression $ (a + b) c - d $ given $a=1$, $b=2$, $c=3$, and $d=4$. 2. **Write the formula:** The expression is $ (a + b) c - d

1. The problem is to find the equation of the line passing through the points $(4,-3)$ and $(3,-6)$.\n\n2. The formula to find the slope $m$ of a line through two points $(x_1,y_1)

1. **Problem statement:** (a) Factorise completely the expression $x^3 - 4x$.

1. **State the problem:** Solve the quadratic equation $x^2 + 5 - 6 = 0$. 2. **Simplify the equation:** Combine like terms:

1. **بيان المسألة:** لدينا الدالة $$f(x) = \frac{2a - x^2}{x}$$ حيث $$a > 0$$ و $$x \neq 0$$. مطلوب حل البنود التالية: 2. **إيجاد معادلات خطوط التقارب المماسة للمحورين:**

1. **State the problem:** Solve the equation $$12 \left( \frac{x}{6} + 5 \right) = 5 \left( \frac{x}{5} - 30 \right)$$ for $x$. 2. **Use the distributive property:** Multiply insid

1. **State the problem:** Solve the quadratic equation $x^2 - 18x + 81 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **State the problem:** Simplify the expression $-32 - (-2 - 2 - 1)^2$. 2. **Understand the order of operations:** We first simplify inside the parentheses, then apply the expone

1. **Problem Statement:** Find all possible pairs $(a,b)$ such that the number $48a23b$ is a multiple of 18. 2. **Key Concept:** A number is a multiple of 18 if and only if it is d

1. Soal pertama: Sederhanakan ekspresi \( \frac{8a^{-3} b^5}{2a^6 b^2} \). 2. Gunakan aturan pangkat: \( \frac{a^m}{a^n} = a^{m-n} \) dan \( a^{-m} = \frac{1}{a^m} \).

1. **Problem statement:** The sum of three numbers is 174. The ratio of the second number to the third number is 9:16, and the ratio of the first number to the third number is 1:4.

1. **Problem Statement:** Given that $l^2 + m^2 + n^2 = 1$ and $l'^2 + m'^2 + n'^2 = 1$, find the value of $ll' + mm' + nn'$. 2. **Formula and Explanation:** The expressions $l^2 +

1. The first expression given is $2x - x^2 + 2xy - xy^2$. 2. The second expression to expand and simplify is $(x + a)(x + b) - (x - a)(x - b)$.

1. The problem is to calculate $5$ divided by $\frac{11}{2}$. 2. The formula for dividing by a fraction is to multiply by its reciprocal: $a \div \frac{b}{c} = a \times \frac{c}{b}