🧮 algebra

1. Given the equation $x - 3 = -\frac{1}{x}$, our goal is to find the value of $x^3 + \frac{1}{x^3}$. 2. First, rewrite the equation:

1. Stated problem: Solve the equation $4(a-2) - 3(a+5) = 7$ for $a$. 2. Expand the parentheses:

1. Problema 4: Encontrar la función inversa de $p(x) = 3(2x - 1)^2 + 3$. 2. Para hallar la inversa, empezamos intercambiando $p(x)$ por $y$:

1. The problem asks to calculate 26000 multiplied by 10%.\n2. Recall that 10% as a decimal is $\frac{10}{100} = 0.1$.\n3. Multiply 26000 by 0.1: $$26000 \times 0.1 = 2600.$$\n4. Th

1. **Stating the problem:** Simplify the algebraic expression $r - 5r - 6s + 8s - 15$. 2. **Combine like terms:** Group terms with $r$ and with $s$ separately.

1. State the problem: Find the x-intercepts of the function $$f(x)=3x^3+2x^2-5x-2$$. The x-intercepts occur where $$f(x)=0$$. 2. Set the equation to zero: $$3x^3+2x^2-5x-2=0$$.

1. Problema 7: El 2º término de una progresión geométrica (PG) es $a_2$, y el 5º término es $a_5$. Expresar la progresión. Paso 1: Sea $a_1$ el primer término y $r$ la razón común.

1. Diberikan sistem persamaan $$\frac{3}{x} + \frac{2}{y} = -7 \\

1. समस्या: दुई समसामयिक रेखीय समीकरणहरु 2x + y = 8 र x + y = 5 छन्। यी समीकरणहरुलाई ग्राफ प्रयोग गरेर समाधान गर्नूहोस्। 2. पहिलो समीकरणलाई y को रूपमा अभिव्यक्त गरौँ:

1. Let's clarify the problem: you are asking if the third term (or expression) is at least 2y greater than $\frac{1}{3}x$. 2. To analyze this, we need the exact expression for the

1. Planteamos la ecuación dada: $$\frac{5}{3x - 1} - \frac{1}{5x - 7} = \frac{11x - 1}{15x^2 - 26x + 7}$$

1. Let's translate each statement into a mathematical inequality. 2. "The sum of $x$ and $y$ is at most 10" means the sum cannot be greater than 10. This can be written as:

1. The problem is to solve the equation or expression given. 2. Since no explicit equation or expression was provided, please provide the details of the question you want solved.

1. Diketahui sistem persamaan: $$2^x - 5^y = 7$$

1. Problem: Solve the simultaneous linear equations $2x + y = 8$ and $x + y = 5$ by graphing. 2. Step 1: Identify the system type. These are simultaneous linear equations because t

1. Diketahui fungsi objektif $Z = 12x + 8y$ dengan daerah penyelesaian berbentuk segitiga yang dibatasi sumbu X, sumbu Y, dan sebuah garis. 2. Dari deskripsi, daerah penyelesaian d

1. The user asks to write "these" as inequalities, but no specific expressions or statements were provided. 2. To proceed, please provide the expressions or conditions you want con

1. **Simplify each given expression step-by-step.** 2. Expression: $4x^2 + 4x \times 2x + 5x^2$

1. The problem is to simplify the expression $4a^2b - 4ab^2$. 2. Factor out the common factor in both terms. Both terms have a common factor of $4ab$.

1. The problem is to simplify the expression $4a^2b - 4ab$. 2. Look for common factors in both terms. Both terms share a factor of $4ab$.

1. **State the problem:** Evaluate the expression $$\frac{3^2 \times 3^5}{3^3}$$. 2. **Use the laws of exponents:** When multiplying powers of the same base, add the exponents.