🧮 algebra

1. **State the problem:** Solve the quadratic equation $$x^2 - 4x - 3 = 0$$ for $x$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solu

1. Solve $3 \cdot (5x - 8)$: Multiply 3 by each term inside the parentheses:

1. **State the problem:** Simplify the expression $3 \cdot (5x - 8)$. 2. **Formula and rules:** Use the distributive property: $a(b + c) = ab + ac$. This means multiply each term i

1. Stating the problem: Solve the equation or system given (not specified, so assuming a generic solve request). 2. Since no specific equation was provided, I cannot solve it witho

1. **Stating the problem:** Simplify the expression $$\sqrt{2} \cdot \sqrt[3]{3}$$. 2. **Recall the rules:**

1. **State the problem:** Find the two values of $x$ such that $$x^2 - 14 = 50$$. 2. **Add 14 to both sides to isolate $x^2$:**

1. **State the problem:** Expand the expression $12x(7x + y)$. 2. **Recall the distributive property:** To expand an expression like $a(b + c)$, multiply $a$ by each term inside th

1. **State the problem:** Solve for $f$ in the equation $$3 = 2f + 15$$. 2. **Isolate the variable term:** Subtract 15 from both sides to get the term with $f$ alone on one side.

1. **State the problem:** Solve the equation $$\frac{48}{c-1} = 3$$ for $c$. 2. **Use the formula:** To solve for $c$, multiply both sides of the equation by the denominator $(c-1)

1. **State the problem:** Expand the expression $3(3a + 2b - c)$. 2. **Formula used:** Use the distributive property of multiplication over addition/subtraction: $$a(b + c + d) = a

1. **State the problem:** Solve the equation $$6 = 18 + \frac{h}{3}$$ for the variable $h$. 2. **Isolate the term with $h$:** To solve for $h$, first subtract 18 from both sides:

1. **State the problem:** Solve the equation $$\frac{x + 51}{7} + 24 = 35$$ for $x$. 2. **Isolate the fraction:** Subtract 24 from both sides to get $$\frac{x + 51}{7} = 35 - 24$$

1. **State the problem:** Factorise the expression $$x^2 - 6x + 2x^2 + 7$$. 2. **Combine like terms:** First, combine the terms with $$x^2$$.

1. **State the problem:** We are given the function $$f(x) = 8 - 2x - x^2$$ and need to find the coordinates of points a, b, and c on its graph. 2. **Understand the function:** Thi

1. **Problem statement:** Simplify each expression, leaving the answer in index form. 2. **Important rules:**

1. The problem is to solve the equation or expression given by the user, but since no specific equation was provided, I will demonstrate solving a simple algebraic equation as an e

1. Laten we het probleem formuleren: we moeten een algebraïsche vergelijking oplossen of een wiskundig concept uitleggen (u heeft geen specifieke vraag gesteld, dus ik wacht op uw

1. **State the problem:** Simplify the expression $$w = \frac{(-2^{-3})^{-3}}{(2^{-2})^{-4}}$$. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{(-2^{-3})^{-3}}{(2^{-2})^{-4}}$$. 2. **Recall the power of a power rule:** For any base $a$ and exponents $m$ and $n$, $$(

1. **Énoncé du problème :** Résoudre l'inéquation $$(x - 1)(2x + 4) + (x - 1)(x - 3) > 0$$ 2. **Formule et règles importantes :** Pour résoudre une inéquation produit, on factorise

1. Das Problem: Wir wollen wissen, wie man eine Gleichung in die Standardform bringt. 2. Die Standardform einer linearen Gleichung in zwei Variablen ist $$Ax + By = C$$, wobei $$A$