🧮 algebra

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **Énoncé du problème :** Remplir un carré magique multiplicatif 3×3 avec des puissances de $a$ et $b$ données, de sorte que le produit de chaque ligne, colonne et diagonale soit

1. **State the problem:** We need to rewrite the quadratic function $$g(x) = 5x^2 + 20x - 12$$ in the form $$g(x) = a(x + h)^2 + k$$ where $$a, h, k \in \mathbb{Z}$$. 2. **Recall t

1. **State the problem:** Multiply and divide the rational expressions: $$\frac{4x^3+4x^2}{2x} \div \frac{x^2-1}{x^2+2x-3} \cdot \frac{x+3}{x^2+3x}$$

1. **State the problem:** Multiply and divide the rational expressions: $$\frac{x-1}{x^2+5x+6} \cdot \frac{x^2+x-2}{3} \div \frac{x-1}{3x}$$

1. **State the problem:** Solve the equation $$-\frac{1}{2} = 3 - \left(\frac{1}{2}x - 10\right)$$ for $x$ and write the answer in simplest form. 2. **Rewrite the equation:**

1. **Problem 9:** Find the equation of an equilateral hyperbola with foci at $(\sqrt{2},0)$ and $(-\sqrt{2},0)$. - An equilateral hyperbola has equal transverse and conjugate axes,

1. **State the problem:** Solve the inequality $$w + 3 \leq -10$$ and determine if $$w = -13$$ is a solution to the inequality. 2. **Rewrite the inequality:** To isolate $$w$$, sub

1. **State the problem:** Solve the inequality $w + 3 \leq -10$. 2. **Find the boundary point by solving the equation:**

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