🧮 algebra

1. **State the problem:** We have a line $l$ passing through the point $(4,2)$.

1. **Planteamiento del problema:** Se nos dan las matrices

1. **State the problem:** Solve the two-step linear equation $$-2 = 2v - 4$$ for the variable $v$. 2. **Write the formula and rules:** To solve for $v$, we need to isolate $v$ on o

1. **State the problem:** Find the least common multiple (LCM) of the numbers 3, 9, and 12. 2. **Recall the formula and rules:** The LCM of a set of numbers is the smallest positiv

1. **State the problem:** Solve the two-step linear equation for $y$: $$-2 = 2y - 4$$ 2. **Formula and rules:** To solve for $y$, isolate the variable by undoing addition/subtracti

1. **State the problem:** Solve the linear equation $2x - 2y = 12$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to rearrange the equation by moving te

1. **State the problem:** We need to find the volume of a gold bar shaped like a rectangular prism with dimensions 6 in. × 2 \frac{7}{8} in. × 1 \frac{1}{2} in., then use the formu

1. The problem states: Solve for $z$ in the equation $\log_7 z = 3$. 2. Recall the definition of logarithm: $\log_b a = c$ means $b^c = a$.

1. **State the problem:** We need to solve for $n \in \mathbb{N}$ the equation

1. **State the problem:** Show that $\left(\log_2 3\right)\left(\log_3 4\right) = 2$. 2. **Recall the change of base formula:** For any positive numbers $a,b,c$ with $a \neq 1$ and

1. **State the problem:** Determine whether $x$ and $y$ show direct variation, inverse variation, or neither for equations 4 to 11. 2. **Recall definitions:**

1. **State the problem:** Calculate the value of $\frac{21}{3} - \frac{25}{6}$. 2. **Find a common denominator:** The denominators are 3 and 6. The least common denominator (LCD) i

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