🧮 algebra

1. **State the problem:** We need to solve the system of inequalities by graphing: $$y \leq 1$$

1. The problem asks us to find the value represented by the symbol \tealD6 in the number $$97\tealD6.14$$. 2. Since \tealD6 is used in a number with digits before and after the dec

1. **State the problem:** We need to graph the rational function $$f(x) = \frac{-x + 5}{-2x + 1}$$ and identify its vertical and horizontal asymptotes. 2. **Find vertical asymptote

1. **Problem Statement:** Given a rational function $f$ with a vertical asymptote at $x=0$ and a horizontal asymptote at $y=2$, find the equations of the asymptotes, the $x$- and $

1. Let's consider a simple algebra problem: Solve for $x$ in the equation $$2x + 3 = 7$$. 2. The formula to solve for $x$ in a linear equation $ax + b = c$ is to isolate $x$ by sub

1. **Problem Statement:** Create an algebraic expression with at least three unlike terms and simplify it. 2. **Step 1: Write an expression with unlike terms.**

1. El problema pregunta si para una matriz invertible $A$, la matriz $A + A^{-1}$ siempre es invertible. 2. Recordemos que una matriz $A$ es invertible si existe $A^{-1}$ tal que $

1. Planteamos el problema: Tenemos dos parábolas, $P_1$ y $P_2$. La parábola $P_2$ tiene vértice en el origen $(0,0)$ y pasa por el punto $(2,1)$. La parábola $P_1$ pasa por los pu

1. **State the problem:** We need to find the slope of the line passing through the points $(-3, -2)$ and $(4, 4)$. 2. **Formula for slope:** The slope $m$ of a line passing throug

1. Planteamos el problema: Encontrar los enteros $m$ tales que $\ln(m+3)$ y $\ln(10-2m)$ estén definidos. 2. Recordemos que el logaritmo natural $\ln(x)$ está definido solo para $x

1. **State the problem:** Find the equation of the line passing through the points $(-6,4)$ and $(-2,2)$ in slope-intercept form $y=mx+b$. 2. **Formula used:** The slope $m$ of a l

1. **Stating the problem:** We are given matrices:

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} -3 & \text{if } x \leq -2 \\ x - 1 & \text{if } -2 < x \leq 2 \\ 0 & \text{if } x > 2 \end{cases

1. **State the problem:** Solve the equation $12 - 4x = -7x$ for $x$. 2. **Recall the rule:** To solve linear equations, isolate the variable on one side by performing the same ope

1. **State the problem:** We need to find the number of solutions to the equation $$-9 + 7(-2n + 6) = -19 - 14n$$. 2. **Use the distributive property:** Multiply 7 by each term ins

1. **State the problem:** We need to find how many solutions the equation $$12 - 10u = -2 - 10u + 14$$ has. 2. **Simplify both sides:**

1. **State the problem:** Solve the equation $$12 - 20q = 4(-6q - 17)$$ and determine how many solutions it has. 2. **Write the equation:** $$12 - 20q = 4(-6q - 17)$$

1. **State the problem:** Find the number of solutions to the equation $$13g - 3g + 19 = 5 + 10g$$. 2. **Simplify both sides:** Combine like terms on the left side:

1. **State the problem:** Solve the equation $$-16y + y + 20 = -15y + 20$$ and determine how many solutions it has. 2. **Simplify both sides:** Combine like terms on the left side:

1. **State the problem:** Solve the linear equation $-4x + 15 = -9x - 15$ for $x$. 2. **Write down the equation:**

1. **Problem Statement:** We have a square and an equilateral triangle with the same perimeter.