🧮 algebra

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 $ab$.

1. Énoncé du problème : Développer l'expression $A = (2x - 1)^3$. 2. Formule utilisée : Pour développer un cube de binôme, on utilise la formule

1. **Stating the problem:** Solve the equation $$\sqrt{x^3 + x^2 - 1} + \sqrt{x^3 + x^2 + 2} = 3.$$\n\n2. **Understanding the problem:** We have two square root expressions added t

1. **Problem statement:** Solve the equation $$\sqrt{4x^2 + 5x + 1} - 2\sqrt{x^2 - x + 1} = 9x - 3.$$\n\n2. **Step 1: Understand the equation and domain.**\n- The expressions under

1. **State the problem:** Solve the equation $ak^2 - xy = 3$ for one of the variables or express it in a useful form. 2. **Understand the equation:** This is an algebraic equation

1. **State the problem:** We are given the equation $a k 2 - x y = 3$ and need to understand or solve it.

1. **Énoncé du problème :** Écrire sous forme d’une puissance l’expression $$4 = \left(\frac{2}{3}\right)^{-3} \times \left(\frac{3}{7}\right)^{-2}$$.

1. **Énoncé du problème :** Écrire sous la forme $a + b\sqrt{c}$ avec $a,b,c$ entiers les expressions suivantes :