🧮 algebra

1. **State the problem:** Determine whether $x$ and $y$ show direct variation, inverse variation, or neither for the equations given. 2. **Recall definitions:**

1. Risolviamo la disequazione $x^2 - 25 > 0$. Fattorizziamo: $$x^2 - 25 = (x - 5)(x + 5)$$

1. Resolveremos la ecuación dada para encontrar el resultado. 2. Aplicamos las operaciones necesarias para simplificar y despejar la variable.

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **Stating the problem:** Risolviamo l'equazione $$404. -14 + \frac{3(3x+6)^2}{4} - (3x+4)^2 = -\frac{(3x-6)^2}{4}$$ 2. **Formula and rules:** Per risolvere equazioni con termini

1. **State the problem:** Simplify or factor the expression $a^3 + c^3$ given the sum $a + c$. 2. **Formula used:** The sum of cubes factorization formula is:

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. Enunciamo il problema: risolvere l'equazione $\frac{2x+4}{3} = \frac{x-1}{2}$.\n\n2. La formula da usare è la proprietà fondamentale delle equazioni: se $\frac{a}{b} = \frac{c}{

1. **State the problem:** Calculate the sum of $2.8 \times 10^{6}$ and $11 \times 10^{6}$ and express the answer in scientific notation. 2. **Formula and rules:** When adding numbe

1. **Problem:** Henri purchased a stereo for 400 and sold it for 450. Find the markup as a percentage of the purchase price. 2. **Formula:** Markup percentage = \( \frac{\text{Sell

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the equati

1. Planteamos el problema: Resolver la ecuación $2x + 3 = 11$. 2. Usamos la fórmula para despejar $x$ en una ecuación lineal: $$ax + b = c \implies x = \frac{c - b}{a}$$ donde $a$,

1. **State the problem:** Solve the system of equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** Solve the equation $$\frac{8}{x + 2} - \frac{5}{3} = \frac{x - 1}{3}$$ for $x$. 2. **Identify the formula and rules:** To solve rational equations, first

1. **State the problem:** Solve the quadratic equation $$f(x) = x^2 - 2x - 3 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solut

1. **State the problem:** Solve the equation $$\frac{8}{x + 2} - \frac{5}{3} = \frac{x - 1}{3}$$ for $x$. 2. **Identify the formula and rules:** To solve rational equations, first

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** We are given the set of ordered pairs \(\{(1, 2), (2, 3), (3, 4), (3, 5), (4, 3)\}\) and asked which coordinate must be removed so that the set represents

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations on both sides of the equation.