🧮 algebra

1. El problema consiste en verificar si las dos fracciones resultantes en los ejercicios a) y b) están correctas. 2. Para el inciso a), la expresión es:

1. **Problem statement:** Find where the linear function $f(x)$ is less than zero ($f(x)<0$) and where it is greater than zero ($f(x)>0$). 2. **Formula and rules:** For a linear fu

1. **Problem statement:** Solve the system of equations: $$\frac{x + y + 3}{x - 2y} + \frac{x - 2y}{x + y + 3} = 2$$

1. **State the problem:** Solve the equation $5 - 13x = 4 + 9x$ for $x$. 2. **Write the formula and rules:** To solve linear equations, we isolate the variable $x$ by performing th

1. The problem is to solve the equation $$3x - 7 = 11$$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We add 7 to both sides to cancel the $

1. **Énoncé du problème :** Factoriser l'expression $$9x^2 + 24x + 16$$, puis factoriser $$A = 9x^2 + 24x + 16 + (3x + 4)(2x - 5)$$ et enfin résoudre l'équation $$A = 0$$.

1. **Problemstellung:** Löse die Gleichung $$-0,5x + 2,5 = 1,5x - 1,5$$ nach $$x$$ auf, um die x-Koordinate des Schnittpunkts der Geraden zu bestimmen. 2. **Formel und Regeln:** Um

1. **Problem statement:** Find the solution of the system of equations:

1. Das Problem lautet: Löse die Gleichung aus Aufgabe 2a. 2. Wir verwenden die allgemeine Methode zum Lösen von linearen Gleichungen: Ziel ist es, die Variable auf einer Seite der

1. **Problem statement:** Berechnen Sie das durchschnittliche jährliche Bevölkerungswachstum in Prozent von 67 279 Menschen am 01.01.2010 auf 81 240 Menschen neun Jahre später.

1. **State the problem:** Solve for $x$ in the equation $$\frac{x + 4}{5} + \frac{2x - 1}{3} = 1.$$\n\n2. **Formula and rules:** To solve equations with fractions, find a common de

1. **State the problem:** Simplify the expression $$2 \times \frac{4}{5} + \frac{14 + 3x}{4}$$. 2. **Apply multiplication:** Multiply 2 by the fraction \(\frac{4}{5}\):

1. **State the problem:** Simplify the expression $$6 \div 2(15 + 20)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. Let's start by stating the problem clearly: You want to understand the simplification step at part 7. 2. Simplification in algebra often involves reducing expressions by canceli

1. **State the problem:** Convert a mixed number to an improper fraction. 2. **Formula:** For a mixed number $a \frac{b}{c}$, the improper fraction is given by:

1. The problem is to solve the equation by isolating $y$ first. 2. Suppose the equation is given in the form $Ax + By = C$.

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$.\n2. Use the formula for solving linear equations: isolate $x$ by performing inverse operations.\n3. Subtract 3 from

1. Solve the system: $$\begin{cases} x + y + z = 6 \\ 2x - y + 3z = 14 \\ -x + 4y - z = 2 \end{cases}$$ 2. Solve the system: $$\begin{cases} 3x + 2y - z = 7 \\ x - y + 4z = 10 \\ 2

1. **Problem Statement:** Solve the system of 10 simultaneous equations with 3 variables $x$, $y$, and $z$ where all solutions are whole numbers. 2. **General Approach:** For simul

1. The problem is to solve the system of equations by eliminating $y$. 2. Suppose the system is:

1. State the problem: Solve the system of simultaneous equations with three variables $x$, $y$, and $z$ where all solutions are whole numbers. 2. Example system: