🧮 algebra

1. **State the problem:** Solve the equation $$\frac{x}{3} - 5 = 1$$ for $x$. 2. **Add 5 to both sides** to isolate the fraction term:

1. **State the problem:** Solve the equation $\binom{x}{2} + 3 = 7$ for $x$. 2. **Recall the formula:** The binomial coefficient $\binom{x}{2}$ is defined as $$\binom{x}{2} = \frac

1. **Planteamiento del problema:** Se necesita saber cuántas mascarillas n95 se pueden comprar con un presupuesto de 15.75, sabiendo que un cartón contiene 13 mascarillas y cuesta

1. **State the problem:** Solve the equation $2(x+3)-x=11$ for $x$. 2. **Write the formula and rules:** Use the distributive property and combine like terms to isolate $x$.

1. Planteamos el problema: Resolver la ecuación cuadrática completa $x^2 - 5x + 6 = 0$. 2. La fórmula general para resolver ecuaciones cuadráticas $ax^2 + bx + c = 0$ es:

1. **State the problem:** Solve the equation $3x + 5 - 2x = 12$ for $x$. 2. **Combine like terms:** On the left side, combine $3x$ and $-2x$.

1. **State the problem:** Simplify the rational expression \( \frac{70m^7n^2 - 50m^5n + 10m^3n^4}{10m^2n} \). 2. **Write the formula:** To simplify, divide each term in the numerat

1. **Problem A:** Perform the subtraction \((x^2 - 3x + 7) - (4 + 5x^2 - x)\). 2. Write the expression clearly:

1. The problem is to simplify the expression $10x^2 \sqrt{x}$. 2. Recall that $\sqrt{x} = x^{\frac{1}{2}}$.

1. **State the problem:** Simplify the expression $10x^2 \sqrt{x^5 - 3}$. 2. **Recall the formula and rules:** The square root of a product can be written as the product of square

1. The problem is to simplify the expression 10$x^2$. 2. The expression consists of a constant multiplier 10 and a variable term $x^2$.

1. **State the problem:** Jet wants an average of 80% after 5 rounds, each worth 50 points. We know his scores for the first 4 rounds and want to find the minimum score in the 5th

1. The problem asks to convert the improper fraction $\frac{10}{3}$ to a mixed number and the mixed number $4 \frac{11}{12}$ to an improper fraction. 2. To convert an improper frac

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. The problem is to solve the equation $$3x - 7 = 11$$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We add 7 to both sides to cancel the $

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **Перевірка, чи є пара чисел (1; -2) розв’язком системи:** Дано систему:

1. The problem is to list and explain the 7 cases of linear inequalities. 2. Linear inequalities involve expressions like $ax + b > 0$, $ax + b \geq 0$, $ax + b < 0$, $ax + b \leq

1. Stating the problem: We want to find the sum of the integers from 1 to 7. 2. Formula used: The sum of the first $n$ natural numbers is given by the formula $$S = \frac{n(n+1)}{2

1. The problem is to list and explain the 7 cases of linear inequalities. 2. Linear inequalities involve expressions like $ax + b > 0$, $ax + b \geq 0$, $ax + b < 0$, $ax + b \leq

1. The user asks for examples for each, but the question is ambiguous without specifying what "each" refers to. 2. Since no specific topic or category is given, I will provide exam