🧮 algebra

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

1. **State the problem:** Simplify the expression $$2ab^2 \cdot (a^2 - 2ab - 3b^2) - 2ab \cdot (a^2b - 2ab^2 - 6b^3)$$. 2. **Distribute each term:**

1. **State the problem:** Simplify the expression $$2ab^2 \cdot (a^2 - 2ab - 3b^2) - 2ab \cdot (a^2b - 2ab^2 - 6b^3)$$. 2. **Distribute each term:**

1. You asked if I can write a literal expression if you provide a problem. 2. Please provide the specific math problem you want me to write a literal expression for.

1. El problema es calcular la raíz cuadrada aproximada con dos decimales de $32$. 2. Usamos el método de extracción de raíz cuadrada por aproximaciones sucesivas, que consiste en e

1. Problem: Round 0.007856 to 2 significant figures. Step 1: Identify the first 2 significant figures: 7 and 8.

1. **State the problem:** Solve the equation $$-111 = 3(7x - 2)$$ for $x$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** Simplify the expression $$\frac{1 - x}{1 + x} + (1 - x)^2$$ and verify if the given simplification $$1 - x^2 + 1 + x^2$$ is correct. 2. **Recall the formu

1. The problem is to express the height $h$ as a function of time $t$ given by the quadratic equation $$h = -2t^2 + 11t + 6.$$ 2. This is a quadratic function in standard form $h =

1. **Stating the problem:** Develop the equality $$(7x + x^4) \cdot (7x - x^4)$$. 2. **Formula used:** This is a product of conjugates, which follows the identity $$ (a+b)(a-b) = a