🧮 algebra

1. Let's create a similar algebra problem for practice. 2. Problem: Solve for $x$ in the equation $$3x - 7 = 2x + 5$$.

1. **State the problem:** We have two customers buying cheese and milk. The first customer pays 12.45 dollars for 1 pound of cheese and 2 gallons of milk. The second customer pays

1. **State the problem:** Solve the inequality $$\frac{3}{4}(x + 8) > \frac{1}{2}(2x + 10)$$ and graph the solution on a number line. 2. **Write the inequality:** $$\frac{3}{4}(x +

1. **State the problem:** We need to determine which values of $x$ satisfy the inequality $$4(2 - x) > -2x - 3(4x + 1).$$ 2. **Expand both sides:**

1. **State the problem:** Simplify the expression $$(-2)^2 - (-2)(+3) + (-2)^7 : (-2)^4 - [(-2)^8 \times (-2)^2] : (-2)$$ where ":" denotes division. 2. **Recall the rules:**

1. **Problem:** Factorise the quadratic expression $x^2 + 7x + 12$. 2. **Formula and rules:** To factorise a quadratic expression of the form $x^2 + bx + c$, find two numbers that

1. **State the problem:** Simplify the expression $$- \frac{1}{16} : (x+2)(x+2)(x-3)(x-3)$$ which means dividing $$- \frac{1}{16}$$ by the product $$(x+2)^2 (x-3)^2$$. 2. **Rewrite

1. **Problem:** Find $x$ such that $$(x-1)^3 = 4^3$$ 2. **Formula and rules:** For equations of the form $a^3 = b^3$, if $a$ and $b$ are real numbers, then $a = b$.

1. Planteamos el problema: Analizar la función por partes $$F(x) = \begin{cases} x^2 - x, & x \leq 1 \\ x^3 - 8, & 1 < x \leq 2 \end{cases}$$ y graficarla. 2. Para cada rama, ident

1. Problemet är att bestämma alla nollställen till polynomet $$p(x) = 2x^3 + x^2 - 8x + 3$$. 2. För att hitta nollställen löser vi ekvationen $$p(x) = 0$$, alltså:

1. **State the problem:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we can facto

1. **State the problem:** Solve the equation $$\log(2x + 3) + \log(x + 2) - 1 = 0$$ for $x$. 2. **Use the logarithm property:** The sum of logarithms is the logarithm of the produc

1. Bài toán yêu cầu tìm giá trị của $x$ thỏa mãn phương trình $ (x-2)(x-1) = x(2x+1) + 2$.\n\n2. Viết lại phương trình và mở rộng các biểu thức:\n$$ (x-2)(x-1) = x(2x+1) + 2 $$\n$$

1. Bài toán yêu cầu tìm giá trị của $x$ thỏa mãn phương trình $$3(2x-3)+2(2-x)=-3.$$\n\n2. Ta sẽ sử dụng quy tắc phân phối để khai triển các biểu thức trong dấu ngoặc.\n\n3. Khai t

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 18}{x^2 - 4x + 4} \cdot \frac{x - 2}{2(x + 3)}$$

1. The problem is to graph the function $y = x^2$. 2. The formula used is $y = x^2$, which is a quadratic function representing a parabola.

1. **State the problem:** We have a matrix of vehicle counts over three days and a charge matrix for each vehicle type. We want to find which revenue statement is true based on the

1. **State the problem:** We need to find the matrix $A$ given by the equation: $$A = 3.1 \begin{bmatrix} 1 & -4 & 0 \\ -2 & 2 & -1 \end{bmatrix} - 1.2 \begin{bmatrix} -1 & 2 & 5 \

1. El problema es reescribir la ecuación dada $$y = -\frac{1}{2}x - 2$$ en la forma estándar $$Ax + By = C$$, donde $$A$$, $$B$$ y $$C$$ son números enteros. 2. La forma estándar d

1. **State the problem:** Solve the equation $$0=36x^4+60x^3-696x^2-480x$$ algebraically using the factor theorem and polynomial long division. 2. **Rewrite the equation:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-125} \times (1 - 0.8)^2 + 0.3}{(\frac{1}{5})^{-1} - \sqrt{2.25}}$$. 2. **Recall formulas and rules:**