🧮 algebra

1. **State the problem:** Solve the equation $$\frac{6}{x+6} = \frac{4}{7}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, we use cross-multiplication:

1. **State the problem:** Solve the equation $$\frac{6}{x} + 6 = \frac{4}{7}$$ for $x$. 2. **Isolate the fraction term:** Subtract 6 from both sides:

1. **State the problem:** Solve the equation $\frac{15}{27} = \frac{2x}{x+26}$ for $x$. 2. **Write the equation:**

1. **State the problem:** Simplify the expression $$\sqrt{(3y^2)^2} \cdot \left(\sqrt{3y^2}\right)^2$$. 2. **Recall the properties of square roots and exponents:**

1. **State the problem:** Simplify the expression $$23 - \frac{3}{4} (\sqrt{150a})^{2} \cdot 8a \sqrt{242a^{2}}$$. 2. **Recall important rules:**

1. **Stating the problem:** We are given the equation $$\sqrt{x^2 + y^2} = 1$$ which represents a graph. 2. **Understanding the formula:** The expression $$\sqrt{x^2 + y^2}$$ repre

1. **Problema:** Dividir el polinomio $x^2 + 5x + 6$ entre $x + 2$. 2. **Fórmula y regla:** Para dividir polinomios, usamos la división larga o división sintética. Aquí usaremos di

1. Stating the problem: Simplify the expression $-x^{2}y + x^{2}y$. 2. Formula and rules: When adding or subtracting like terms, combine their coefficients and keep the variable pa

1. **State the problem:** Simplify the expression $1 \left(\frac{1}{5}\right) m^{4-n} \cdot 0.5 m^{n+6}$. 2. **Rewrite the expression:**

1. **State the problem:** Find the value of the expression $$4a^{2} - ab$$ for $$a = 1.47$$ and $$b = 5.78$$. 2. **Write the formula:** The expression is $$4a^{2} - ab$$.

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

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

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

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

1. State the problem: Solve the system $2x+3y=7$ and $x-y=1$, then find $x+y$. 2. Write the system clearly:

1. El problema nos pide calcular el valor numérico del polinomio $$P(x,y) = 4x^2 y^3 - 3x^3 y^2$$ para $$x=3$$ y $$y=4$$. 2. La fórmula del polinomio es:

1. **State the problem:** Calculate the cube root of 64, written as $\sqrt[3]{64}$. 2. **Formula and rule:** The cube root of a number $a$ is a number $b$ such that $b^3 = a$. So,

1. State the problem: Solve for $a$ in $a^3+a^2=36$. 2. Start with the given equation:

1. **Planteamiento del problema:** Tenemos la ecuación $0.4D = \frac{3}{2}H$ y queremos despejar $D$ en función de $H$. 2. **Fórmula y reglas importantes:** Para despejar una varia

1. **State the problem:** Calculate the exact value of $$4 \frac{1}{5} - \left(1 \frac{1}{9} \times 3\right)$$. 2. **Convert mixed numbers to improper fractions:**

1. Planteamos el problema: Simplificar y resolver la expresión algebraica $-2x^2 + 4x - 8$. 2. Observamos que la expresión es un trinomio cuadrático de la forma $ax^2 + bx + c$ con