🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2}{3x} + \frac{1}{7x}$$ and leave the answer in its simplest form. 2. **Identify the common denominator:** Both terms have

1. The problem is to multiply two variables, $x_i$ and $f_i$. 2. When multiplying variables, you simply write them together as a product: $x_i \times f_i = x_i f_i$.

1. **State the problem:** We are told that $y$ varies jointly with $x$ and $z$, and that $y=30$ when $x=5$ and $z=3$. We want to find the general formula for $y$ in terms of $x$ an

1. Let's start by understanding the problem: you want to learn how to solve quadratic sequences, cubic sequences, and geometric sequences. 2. **Quadratic sequences** follow the pat

1. **State the problem:** Solve the linear equation $2x + 5 = 17$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 5 from

1. Let's start with the basics of algebra, which is the branch of math dealing with symbols and the rules for manipulating those symbols. 2. The simplest algebraic expressions invo

1. **State the problem:** Solve the inequality $$12[2 - x] \leq 9[3 - 2x]$$. 2. **Distribute the constants:** Multiply inside the brackets:

1. The problem is to solve the equation $2x = 4$ for $x$. 2. The formula used here is to isolate $x$ by dividing both sides of the equation by the coefficient of $x$, which is 2.

1. **State the problem:** Solve for $x$ in the equation $5x + 3 = 13$. 2. **Write the equation:**

1. **State the problem:** Solve the inequality $$12[2 - 9c] \leq 9[3 - 2d]$$ for variables $c$ and $d$. 2. **Distribute the constants inside the brackets:**

1. The problem asks to solve questions 20 to 26, but per instructions, we will solve only the first question, number 20. 2. Question 20: Calculate $11 \times 27$.

1. **State the problem:** Solve the multiplication $4 \times 38$ using the distributive property. 2. **Formula and rule:** The distributive property states that for any numbers $a$

1. 問題陳述： 我們有一個方程組或問題，其中第一題的第二個解是（8，13）。

1. **State the problem:** Simplify the expression $2(4x+1)9$. 2. **Understand the expression:** The expression involves multiplication of $2$, the quantity $(4x+1)$, and $9$.

1. **State the problem:** The total enrollment in the school is 432 students. The ratio of boys to girls is 5:4. We need to find how many more boys than girls are in the school. 2.

1. **State the problem:** We have a total of 432 students in a school with a ratio of boys to girls as 6:4. We need to find how many more boys than girls are in the school. 2. **Un

1. Énonçons le problème : Trouver la valeur de l'expression $\frac{2-x}{5x}$ lorsque $a=\frac{1}{2}$. 2. Remplaçons $x$ par $a=\frac{1}{2}$ dans l'expression :

1. The problem states that the temperature $t$ in a freezer must be at most $-10$ degrees Fahrenheit. 2. "At most" means the temperature can be less than or equal to $-10$.

1. **State the problem:** We need to find all values of $n$ from the given list that satisfy the inequality $$\frac{1}{3}n > \frac{2}{5}.$$ 2. **Write the inequality and isolate $n

1. Planteamos el problema: Un arquitecto vende dos lotes de terreno, cada uno por 43700 dólares. En el primer lote obtiene una ganancia del 15 % y en el segundo una pérdida del 5 %

1. Stating the problem: We are given the equation $$(x+a)^2 = x^2 + 22x + b$$ and need to find the values of $a$ and $b$. 2. Use the formula for expanding a binomial square: $$(x+a