🧮 algebra

1. **State the problem:** Solve the inequality $4x - 1 < 12x - 11$. 2. **Recall the rule:** To solve inequalities, we isolate the variable on one side. When subtracting or adding t

1. Bài toán yêu cầu tạo ra một đề toán tương tự với một bài toán đã cho (giả sử bài toán gốc là giải phương trình bậc hai hoặc tính giá trị biểu thức). 2. Để ra đề tương tự, ta cần

1. **State the problem:** Solve the inequality $4x - 1 < 12x - 1$. 2. **Write the inequality:**

1. **State the problem:** We need to prove algebraically that the sum of $\frac{1}{2}n(n+1)$ and $\frac{1}{2}(n+1)(n+2)$ is always a square number, where $n$ is an integer.

1. **State the problem:** We have a room where the length is $\frac{3}{2}$ times the breadth. The cost of carpeting the floor is 17550 at 3.25 per m², and the cost of papering the

1. Masalah ini meminta kita menentukan dua angka yang hilang dalam deret angka berikut: 100 ; -10 ; __ ; __ ; 1 ; -1 ; 0.1 ; 2 ; 0.01 ; 4. 2. Perhatikan pola perubahan angka dari s

1. Masalah: Tentukan angka yang hilang dalam seri berikut: 11 ; 14 ; 7 ; __ ; 25 ; 30 ; 35 ; 41 2. Perhatikan pola perubahan angka dalam seri tersebut.

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula to solve for $x$ in a linear equation like this is to isolate $x$ on one

1. The problem is to simplify the expression $ax - by$. 2. This expression is already in its simplest form because it is a linear combination of two variables $x$ and $y$ with coef

1. **State the problem:** Solve for $x$ in the equation $$5^{3x - 7} = 3^{3x - 7}.$$\n\n2. **Understand the equation:** Both sides have the same exponent $3x - 7$, but different ba

1. **Problem:** Given the equation $$24^x - 2 \tan(3x) - 10^x = 14^x$$ with $$x \leq 5 \times 90^\circ$$, find the value of $$x$$ correct to the nearest whole number. 2. **Formula

1. **Stating the problem:** Find the value of $\frac{a}{b}$ given that $$\lim_{x \to -1} \frac{x+3}{x^3 + ax + b} = +\infty.$$

1. Let's start by understanding the problem: You want to know why we use variables like $a$ and $b$ when combining fractions and what happens when we combine them. 2. When combinin

1. **Problem Statement:** Find the sum $$S=\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\cdots+\frac{1}{n(n+1)}$$ and understand why the term $$\frac{1}{k(k+1)}$$ is

1. **Stating the problem:** Find the equation of the line passing through points A(4,9) and B(5,7), and find the x-intercept of this line. 2. **Formula for the equation of a line t

1. **State the problem:** Solve the equation $3^x - 2 = 5^{x+1}$ for $x$. 2. **Rewrite the equation:** The equation is $3^x - 2 = 5^{x+1}$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{561^2 - 459^2}}{4 \times \frac{2}{7} \times 0.15 + 4 \times \frac{2}{7} \div \frac{20}{3}} + 4\sqrt{10} \div \left(\

1. The problem is to find the average (mean) of the numbers 80, 95, and 76. 2. The formula for the average of $n$ numbers $x_1, x_2, ..., x_n$ is:

1. **State the problem:** Solve for $x$ in terms of $a$ from the equation: $$7a \cdot 9b - 1 \cdot x + 9a - 1 - 0 = 0$$

1. The problem asks to find the set of values $x$ such that both inequalities hold: $$x^2 + x - 2 > 0 \quad \text{and} \quad x^2 - 2x - 3 \geq 0$$

1. **State the problem:** Solve for $x$ in the equation $11 \times 10^3 = x^3$. 2. **Write the equation:**