🧮 algebra

1. **State the problem:** Simplify the expression $\frac{X}{3} + 5$ or rewrite it in a clearer form. 2. **Understand the expression:** The expression consists of a fraction $\frac{

1. **State the problem:** Determine the domain and range of the function $$y=\frac{1}{x-3}$$. 2. **Recall the domain rules:** The domain of a function is all the possible input val

1. **State the problem:** Solve the linear equation $7x - 4 = 24$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Add or subtract

1. **State the problem:** Solve the equation $$7(3^x) + 3^x + 3^x = 9^x \times 27(3^x) \times 9(3^x)$$ for $x$. 2. **Rewrite terms with common bases:** Recall that $9 = 3^2$ and $2

1. **State the problem:** Solve the equation $$\frac{12}{x^2-1} = 1$$ for $x$. 2. **Recall the formula and rules:** The denominator $x^2-1$ can be factored using the difference of

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Simplify the expression $$\frac{3^{n+2}}{3^{n+3} - 3^{n+1}}$$. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve for $x$ in the equation:

1. Problem: Determine whether the function $f(x) = -5x + 10$ is one-to-one. 2. A function is one-to-one if each $y$ value corresponds to exactly one $x$ value.

1. **Nêu bài toán:** Cho các số $x, y$ thỏa mãn hệ phương trình $$\frac{x}{3} = \frac{y}{4}$$ và $$y^2 - x^2 = 28.$$ Tìm giá trị của $x$. 2. **Phân tích và sử dụng công thức:** Từ

1. **Nêu bài toán:** Cho các số $x, y$ thỏa mãn hệ phương trình: $$\frac{x}{2} = \frac{y}{7}$$

1. Bài toán yêu cầu tìm giá trị của $a + b$ khi biết $\frac{a}{6} = \frac{b}{4} = 2$.\n\n2. Ta có thể đặt $\frac{a}{6} = 2$ và $\frac{b}{4} = 2$.\n\n3. Từ đó, ta tìm được $a$ và $b

1. Bài toán yêu cầu kiểm tra xem giá trị $x=\frac{5}{6}$ có thỏa mãn tỉ lệ thức $\frac{x}{3} = \frac{2}{5}$ hay không. 2. Tỉ lệ thức là một phương trình dạng $\frac{a}{b} = \frac{c

1. **Problem Statement:** For three consecutive homework assignments, each assignment has one more question than the previous one. The total number of questions on the three assign

1. **State the problem:** Solve the equation $$\frac{V-9}{903} + \frac{V-15}{1195} + \frac{V}{822} = 0.$$\n\n2. **Identify the formula and approach:** We want to find the value of

1. **State the problem:** We want to find the group size $x$ (where $x \geq 25$) that maximizes the revenue for a travel agency. The price per person decreases by 10 for each perso

1. The problem is to understand why the value 65 was used instead of 47 for $f(0)$. 2. When evaluating a function at a specific input, such as $f(0)$, you substitute $0$ into the f

1. সমস্যাটি হলো: একটি সরলরেখার সমীকরণ নির্ণয় করা যা বিন্দু $A(2,3)$ দিয়ে যায় এবং ঢাল $m=4$। 2. সরলরেখার সমীকরণ সাধারণত হয়: $$y = mx + c$$ যেখানে $m$ ঢাল এবং $c$ $y$-অক্ষের ছেদ।

1. **Problem statement:** Solve the quadratic equations by completing the square. 2. **Formula and rules:** To complete the square for an equation $x^2 + bx + c = 0$, rewrite as $x

1. **Problem Statement:** Calculate the simple interest for 50,000 taka at 9% annual interest rate for 1 year and 1 month. 2. **Formula for Simple Interest:**

1. **Problem statement:** Solve the system of equations using Cramer's Rule: $$\begin{cases} 2x + 3y - z = 5 \\ -x + 4y + 2z = 6 \\ 3x - y + z = 4 \end{cases}$$