🧮 algebra

1. **State the problem:** Solve the inequality $-4 + 2x \geq 1$. 2. **Add 4 to both sides:**

1. **Statement of the problem:** We have a sequence $(u_n)$ defined by $u_0 = -1$ and the recurrence relation $$u_{n+1} = \frac{3}{2} u_n - 1.$$ We define another sequence $(v_n)$

1. **Problem Statement:** Simplify the expression $\frac{7x^2}{4} - 3$. 2. **Formula and Rules:** This is a simple algebraic expression involving a fraction and subtraction. No spe

1. **State the problem:** We are given an arithmetic progression (A.P.) where the sum of the 5th and 12th terms is 93, and the 8th term is 43. We need to find the first four terms

1. Simplify each expression and express with positive exponents. **a)** Simplify $\left(\frac{a^3}{b^{-4}}\right)^{-2}$

1. **Énoncé du problème :** Simplifier l'expression $$\ln\left(\frac{1}{2}\right) + \ln\left(\frac{2}{3}\right) + \ln(5)$$. 2. **Formule utilisée :** La somme des logarithmes de pr

1. **Simplify:** $\ln\left(\frac{1}{2}\right) + \ln\left(\frac{2}{3}\right) + \ln(5)$ 2. Use the logarithm property: $\ln(a) + \ln(b) = \ln(ab)$.

1. حل المعادلة $2x + 3 = 7$: $$2x + 3 = 7$$

1. نُعطى الشعاعين $$\mathbf{u} = \begin{pmatrix}1 \\ 3\end{pmatrix}$$ و $$\mathbf{v} = \begin{pmatrix}z^2 - 1 \\ z + 1\end{pmatrix}$$ ونريد إيجاد قيمة العدد الحقيقي $$w$$ بحيث $$\m

1. **State the problem:** Expand and fully simplify the expression $y(6y + 2) + 5(2y + 4)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the f

1. **State the problem:** Expand and simplify the expression $2(w - 1) + 5(2w + 3)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor o

1. **State the problem:** Simplify the expression $10x^2 - (x-2)x^2 - (x+8)$. 2. **Distribute and expand:** Apply the distributive property to the terms inside the parentheses:

1. Problem: Write equations for the given relationships. - w is directly proportional to v.

1. **State the problem:** We need to translate the statement "a varies inversely with b" into an equation. 2. **Recall the formula for inverse variation:** If a quantity $a$ varies

1. **Problem:** Translate "w is directly proportional to v" into an equation. 2. **Formula:** Direct variation means $w = kv$ where $k$ is the constant of proportionality.

1. The problem is to add more steps to a solution, but since no specific problem was given, I will demonstrate adding steps to a simple algebraic equation solving process. 2. Consi

1. **State the problem:** We have a line $n$ passing through points $(-2,5)$ and $(1,-1)$.

1. **Énoncé du problème** : Résoudre dans $\mathbb{R}$ les équations suivantes : (E1) : $\frac{6x - 2}{3x + 4} = 2$

1. The question asks: "Where did the second 5 come from?" This usually refers to an expression or equation where the number 5 appears twice. 2. To answer this, we need to see the o

1. Let's start with a basic Grade 10 Indonesian mathematics topic: solving linear equations. 2. Problem: Solve the equation $3x + 5 = 20$ for $x$.

1. The user asks for questions suitable for grade 7. 2. Since the request is for questions and not a specific math problem, I will provide a sample algebra question appropriate for