🧮 algebra

1. Planteamos el problema: Graficar la función $f(x) = 2x + 1$ y determinar su dominio y recorrido. 2. Recordemos que para funciones lineales de la forma $f(x) = mx + b$, el domini

1. Planteamos el problema: Dada la función $f(x) = \frac{1}{x}$, debemos encontrar las imágenes de $x = -1$ y $x = 2$. 2. Recordemos que la imagen de un valor $x$ en una función $f

1. Problema: Encontrar las imágenes de $-1$ y $2$ para cada función dada. 2. Regla general: La imagen de un valor $x$ en una función $f$ es $f(x)$, es decir, sustituimos $x$ en la

1. **State the problem:** Simplify or factor the quadratic expression $2x^2 - 3x - 35$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two number

1. The problem is to add the mixed number $1 \frac{2}{3}$ and the fraction $\frac{3}{5}$. 2. First, convert the mixed number to an improper fraction. The formula is $a \frac{b}{c}

1. **State the problem:** Factor the quadratic expression $6x^2 + 11x + 3$ using the decomposition method. 2. **Recall the decomposition method:** We look for two numbers that mult

1. **State the problem:** Drew places 11 less than 3 times the number of pieces Larry places. Drew places at least 10 pieces. We need to find how many pieces Larry places. 2. **Def

1. **State the problem:** We are given the 15th term ($T_{15}$) and the 31st term ($T_{31}$) of an arithmetic series and need to find the first term ($a$) and common difference ($d

1. **Problem statement:** We are given an arithmetic series where the 15th term is 43 and the 31st term is 183. We need to find: a) The first term ($a_1$) and the common difference

1. The problem asks to solve the addition and subtraction of fractions and mixed numbers. 2. Let's solve number 5: $$\frac{7}{10} + \frac{7}{8}$$

1. **State the problem:** Solve the system of equations by graphing: $$y = -2x + 8$$

1. **State the problem:** Evaluate the expression $(-4)^5 \cdot 8^4$. 2. **Recall the rules:**

1. **State the problem:** Identify which expression correctly represents the product $(-4) \cdot (-4) \cdot (-4) \cdot (-4) \cdot (-4)$ using exponents. 2. **Recall the exponent ru

1. **State the problem:** We need to find the intercepts of the line given by the equation $x - 6y = 24$ to help graph it. 2. **Recall the intercepts:**

1. The problem asks to write $n^4 \cdot n^2$ without exponents and then express it as $n^\square$. 2. Recall the rule for multiplying powers with the same base: $$a^m \cdot a^n = a

1. **State the problem:** Ritchie wants to paint his bedroom ceiling and four walls. Each surface is 8 feet by 8 feet. We need to find an expression for the number of gallons of pa

1. **State the problem:** We need to find which inequality corresponds to the graph of a line passing through points (-3, -4) and (4, 3) with shading above the line and the inequal

1. **State the problem:** Solve the equation $$\frac{1}{k} + \frac{5}{12} = \frac{6}{5}$$ for $k$. 2. **Isolate the term with $k$:** Subtract $\frac{5}{12}$ from both sides:

1. **State the problem:** We are given two linear relations with data points for number of days and savings. We need to complete the tables, calculate the slopes, and compare the t

1. **State the problem:** We need to solve the system of equations graphically: $$y = x + 4$$

1. The first problem is to solve the equation $0 \div c = 8$. 2. Division by a number $c$ means finding a number which when multiplied by $c$ gives the dividend. Here, $0 \div c =