🧮 algebra

1. **State the problem:** We are given two linear equations:

1. El problema es resolver la ecuación $$\frac{1}{6} = \left(\frac{5}{6}\right)3^{-1} (5)^2$$. 2. Primero, recordemos que $$3^{-1} = \frac{1}{3}$$.

1. The problem is to factor the expression $12x^2 + 8$. 2. To factor an expression, we look for the greatest common factor (GCF) of the terms.

1. **State the problem:** Solve the equation $$12 \times \frac{120}{n + 5} = 12 \times \frac{120}{n} - 24$$ for $n$. 2. **Write the equation clearly:**

1. **State the problem:** Solve the equation $$12 \times \frac{120}{n + 5} = 12 \times \frac{120}{n} - 24$$ for $n$. 2. **Write the equation clearly:**

1. **State the problem:** Simplify the expression $$\frac{4}{35} a^2 b - \frac{12}{5} a b + \frac{8}{15} a^2 b^3 - \frac{16}{25} a^3 b.$$ 2. **Group like terms:** Group terms with

1. **State the problem:** We need to check if $\frac{1}{2} + \frac{3}{10} = \frac{4}{10}$ is true. 2. **Recall the rule for adding fractions:** To add fractions, they must have the

1. **Stating the problem:** We have trapezoid-like shapes with numbers at the bottom corners and numbers at the top, sometimes with an additional number above. We need to analyze t

1. Planteamos el problema: Simplificar la expresión doble sumatoria $$\sum_{n=1}^{\infty} \sum_{k=1}^{2n-1} \frac{(-1)^{k+1} k \cdot a^{k-1} e^{-a} (2n - k + a + 1) \Gamma(2n - k)}

1. **State the problem:** Simplify the expression $\frac{30}{6} \div 2 - 2$. 2. **Recall the order of operations:** Division and multiplication are performed from left to right bef

1. The problem is to understand where the fraction $\frac{1}{2}$ comes from in a given context. 2. Often, $\frac{1}{2}$ appears in formulas involving averages, midpoints, or when c

1. The problem is to understand the variable $y$ and its context. 2. Since no specific equation or context is given, $y$ typically represents a dependent variable in algebra or fun

1. El problema es entender cómo se representa una recta en el plano cartesiano usando su pendiente y su corte con el eje y. 2. La fórmula general para la ecuación de una recta con

1. The problem asks to write the given numbers in standard form (scientific notation). 2. Standard form expresses numbers as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an i

1. Given the problem to solve, we start by writing the equation or expression. 2. Apply the relevant formula or algebraic manipulation.

1. **State the problem:** We have 47 employees in total, with 29 part-time employees. We need to find the percentage of full-time employees. 2. **Identify the number of full-time e

1. The problem is to simplify the expression $$\frac{6}{c+5} + \frac{7}{c+2}$$. 2. To add these fractions, we need a common denominator. The common denominator is $$(c+5)(c+2)$$.

1. **State the problem:** We want to write the expression $$\frac{7}{4} + \frac{5f}{3f+2}$$ as a single fraction in simplest form. 2. **Find a common denominator:** The denominator

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and rules:** To solve a rational equation, multiply both sides by the denominator to eli

1. **State the problem:** We are given two equations:

1. The problem states that $A = \frac{\sqrt{3}}{2} \cdot N$. We want to understand or simplify this expression. 2. This expression means that $A$ is equal to $N$ multiplied by $\fr