🧮 algebra

1. **Identifier le coefficient directeur et l'ordonnée à l'origine** pour chaque fonction affine. Pour une fonction affine $f(x) = ax + b$, $a$ est le coefficient directeur (pente)

1. **State the problem:** We have a table showing input-output pairs and want to find the relationship between "In" and "Out" values. 2. **Given data:**

1. Solve $2x - 18 = 44$. Step 1: Add 18 to both sides to isolate the term with $x$.

1. **State the problem:** Solve for $x$ in the equation $$10 = 1 + \frac{3}{x}$$. 2. **Isolate the fraction:** Subtract 1 from both sides to get $$10 - 1 = \frac{3}{x}$$ which simp

1. **State the problem:** Solve the equation $7x + 4 = 5x - 18$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve for $x$ in the equation $$\frac{a}{x+a} + \frac{1}{x-b} = \frac{a+b}{x+c}.$$\n\n2. **Identify the formula and approach:** To solve for $x$, we need

1. **State the problem:** Simplify the expression $$(4 - x)(3 + 2x)$$. 2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL for binomia

1. **State the problem:** Simplify the expression $$\frac{31^2+15^2}{2}-31\times15$$. 2. **Recall the formula and rules:** This expression involves squares, addition, division, and

1. **State the problem:** Simplify the expression $$(4-x)(3+2x)$$. 2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Solve the equation $$\frac{2}{3}w - \frac{2}{3} = 0$$ for the variable $w$. 2. **Write down the equation:** $$\frac{2}{3}w - \frac{2}{3} = 0$$

1. **Постановка задачи:** Упростить выражение $$\frac{(x-3)^2}{x^3-27} : \frac{x^2-6x+9}{x^2+3x+9}$$. 2. **Запишем деление дробей как умножение на обратную:**

1. The problem involves analyzing the commuter train distance over time given points on a graph. 2. The points provided are (10,15), (20,20), (30,15), (40,0), (50,15), (60,20), (70

1. The problem asks us to find an algebraic expression for "seven times the sum of a number, n, and four." 2. The phrase "sum of a number, n, and four" means we add n and 4: $$n +

1. **State the problem:** We need to find the difference in the amounts Susan and Jim charge for 10 hours of lawn care work. 2. **Analyze Susan's charges:** From the table, Susan's

1. **Problem Statement:** We are given two sets of data representing the relationship between the number of hours worked and the amount charged by two lawn care services: Susan's L

1. Задача: упростить выражение $8x^3 + 0.064y^3$. 2. Формула: заметим, что $8x^3 = (2x)^3$ и $0.064y^3 = (0.4y)^3$.

1. Дано выражение: $ (a+(b-c))^2 $. 2. Используем формулу квадрата суммы: $ (x+y)^2 = x^2 + 2xy + y^2 $.

1. **State the problem:** Simplify the expression $$\frac{16}{32} \times \frac{-24}{72} \times \frac{-12}{-8}$$. 2. **Recall the rules:** When multiplying fractions, multiply the n

1. **State the problem:** Simplify the expression $$\frac{-16}{32} \times \frac{-24}{72} \times \frac{-12}{-8}$$. 2. **Recall the rules:** When multiplying fractions, multiply the

1. **Problem:** Simplify $5(4x + y)$. Formula: Use distributive property $a(b + c) = ab + ac$.

1. Задача: Раскрыть скобки в выражении $$(3a - b)^2 - (3a + b)^2$$. 2. Формула для квадрата разности и суммы: