🧮 algebra

1. **Stating the problem:** We will learn about fractions, how to add, subtract, multiply, and divide them. 2. **What is a fraction?** A fraction represents a part of a whole and i

1. **State the problem:** Solve the equation $$18x + 7 - 14x + (-6x) - 10 = -13$$. 2. **Combine like terms on the left side:** Group the terms with $$x$$ and the constant terms sep

1. The problem is to understand and work with fractions. 2. A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denomi

1. **State the problem:** Solve the quadratic equation $x^2 + 4x + 3 = 0$. 2. **Formula and rules:** The quadratic equation is generally solved using the quadratic formula:

1. **State the problem:** Simplify the expression $3^{-3} \times 27^2 \times (9^4)^{-5}$. 2. **Rewrite all terms with the same base:** Note that $27 = 3^3$ and $9 = 3^2$. So rewrit

1. **State the problem:** We are given a triangle with three angles labeled $x^\circ$, $2x^\circ$, and $(x - 20)^\circ$. We need to write an equation that models the sum of these a

1. **Problem:** Determine the slope of the line passing through the points $(-4, 15)$ and $(2, 6)$. 2. **Formula:** The slope $m$ of a line passing through points $(x_1, y_1)$ and

1. **State the problem:** Solve the system of linear equations: $$2y + x = 3$$

1. **State the problem:** Solve the linear equation $2y + x = 3$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to get $y$ alone on one side of the equa

1. **State the problem:** Solve the equation $2y + X = 3$ for $y$. 2. **Formula and rules:** To isolate $y$, we need to get $y$ alone on one side of the equation. This involves sub

1. **State the problem:** Solve the equation $$3(3x + 2) - 7(3x + 2) = -20$$ for $x$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factors

1. **State the problem:** Solve the equation $$3(3x + 2) - 7(3x + 2) = -20$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factors outside

1. The problem asks to rewrite the quadratic function $y = 4x^2 - 8x + 1$ in vertex form $y = a(x - h)^2 + k$ and then find the product $a \times k$. 2. Recall the vertex form of a

1. **State the problem:** Convert the repeating decimal $-42.1\overline{6}$ to a fraction. 2. **Understand the notation:** The bar over 6 means the digit 6 repeats infinitely: $-42

1. **State the problem:** Convert the repeating decimal $-42.1\overline{6}$ to a fraction. 2. **Understand the notation:** The bar over 6 means the digit 6 repeats infinitely: $-42

1. The problem is to simplify the expression $\sqrt[3]{12}$. 2. The cube root of a number $a$ is a value $b$ such that $b^3 = a$.

1. Ich erstelle dir 3 Probetests zu den Themen lineare Gleichungen mit 2 Variablen und lineare Gleichungssysteme. 2. Jeder Test enthält Aufgaben zu allen wichtigen Verfahren: Gleic

1. **State the problem:** Solve the inequality $$\frac{2x}{(x+2)(x-2)(x-1)} < 0.$$\n\n2. **Identify critical points:** The expression is undefined or zero at points where the numer

1. **State the problem:** Solve the inequality $$|x-3| > 2|3x+1|.$$\n\n2. **Recall the definition of absolute value:** For any real number $a$, $|a| = a$ if $a \geq 0$, and $|a| =

1. The vertex of a parabola given by the quadratic function $y = ax^2 + bx + c$ is found using the formula for the x-coordinate of the vertex: $$x = -\frac{b}{2a}$$ 2. This formula

1. **State the problem:** Identify the vertex, axis of symmetry, min/max value, and y-intercept of the quadratic function $$y = -\frac{1}{4}x^2 - 3x - 10$$. 2. **Recall the standar