🧮 algebra

1. **State the problem:** Simplify the expression $2 + x + 1$. 2. **Combine like terms:** The terms $2$ and $1$ are constants and can be added together.

1. **State the problem:** Solve the inequality $$-15x \leq 2x^2 + 18$$. 2. **Rewrite the inequality:** Move all terms to one side to set the inequality to zero:

1. **State the problem:** Simplify or factor the quadratic expression $6x^2 - 13x - 5$. 2. **Formula and rules:** To factor a quadratic $ax^2 + bx + c$, find two numbers that multi

1. **State the problem:** Simplify or analyze the quadratic expression $x^2 - 13x - 5$. 2. **Formula and rules:** The quadratic expression is in the form $ax^2 + bx + c$ where $a=1

1. **Stating the problem:** We are given the linear function $$y = 18 - 4x$$ and asked to find the value of $$y$$ when $$x = \frac{48}{13}$$. 2. **Formula used:** The function is a

1. **State the problem:** Solve the equation $95 - x = 69$ for $x$. 2. **Formula and rules:** To isolate $x$, we use the rule of adding or subtracting the same number on both sides

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 11$ nach $x$ auf. 2. Die verwendete Formel ist die Umkehrung der Addition und Multiplikation, um $x$ zu isolieren. Wichtig ist,

1. **State the problem:** We are given the absolute value function $$f(x) = |x + 3|$$ and need to express it as a piecewise function. 2. **Recall the definition of absolute value:*

1. **State the problem:** We want to find a system of inequalities that models the minimum population $P$ (in thousands) of crickets over time $t$ (in months). 2. **Understand the

1. **State the problem:** Solve the quadratic equation using the Bhaskara formula (quadratic formula). 2. **Formula:** For a quadratic equation $ax^2 + bx + c = 0$, the solutions a

1. The problem is to find the roots of the function $y(x) = 2(x-1)^2$. 2. Roots of a function are the values of $x$ for which $y(x) = 0$.

1. **Stating the problem:** Find the equations of the lines passing through given points and express them in slope-intercept form $y = mx + b$. 2. **Line R through points $(-2,1)$

1. **State the problem:** Solve the equation $5kx^2 + 6x = 2(x+4)$ for $x$. 2. **Rewrite the equation:** Expand the right side:

1. **Problem Statement:** Find the values of $x$ such that the area of the triangle with vertices $(x,4)$, $(2,-6)$, and $(5,4)$ is 35 square units. 2. **Formula for Area of Triang

1. El problema es simplificar la expresión en un solo cálculo. 2. Para simplificar expresiones algebraicas, se deben aplicar las propiedades de las operaciones y combinar términos

1. **State the problem:** We need to find the slope $m$ and the y-intercept $c$ of the line $T$ given its graph points. 2. **Identify two points on the line:** From the graph, appr

1. Planteamos el problema: Factorizar la función $$f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4$$ y luego aplicar el teorema de Bolzano para encontrar intervalos donde la función cambia de si

1. **Planteamiento del problema:** Dada la función cuadrática $$f(x) = 2x^2 - 4x - 30$$, primero la factorizaremos y luego aplicaremos el Teorema de Bolzano para encontrar un inter

1. **State the problem:** Solve the quadratic equation $$80x^{2} + 9x + 30 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^{2} + bx + c = 0$$ is

1. El problema es convertir una expresión algebraica dada en su forma factorizada. 2. La factorización consiste en expresar un polinomio como el producto de polinomios más simples.

1. **Planteamiento del problema:** Resolver la función $f(x) = x^3 - 5x^2 + 7x - 3$, es decir, encontrar los valores de $x$ para los cuales $f(x) = 0$. 2. **Fórmula y reglas import