🧮 algebra

1. Planteamos el problema: Resolver la inecuación $$8 - 2x - x^2 > 0$$ para encontrar el conjunto solución. 2. Reordenamos la inecuación para tenerla en forma estándar de un polino

1. **State the problem:** Solve the quadratic equation $$x^2 + 9x + 18 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$

1. The problem states the inequality $1 < b$ and provides several values for $b$: 9, 5, 2, and 11. 2. We need to determine which of these values satisfy the inequality $1 < b$.

1. The problem is to determine which values of $b$ satisfy the inequality $1 < b$. 2. The inequality $1 < b$ means that $b$ must be greater than 1.

1. **State the problem:** We need to find which values of $x$ satisfy the inequality $$86 \leq 11x.$$ 2. **Write the formula and rules:** To solve for $x$, we divide both sides of

1. **State the problem:** Solve the quadratic equation $$5x^2 - 6x - 6 = 0$$ by completing the square. 2. **Rewrite the equation:** Move the constant term to the right side:

1. The problem asks: For what values of $x$ is $f(x) = -1$? 2. From the graph description, we look for points where the function's value is $-1$.

1. **State the problem:** The number of bacteria cells doubles every 10 minutes, starting with 1 cell. We want to find the number of cells after 1 hour. 2. **Identify the formula:*

1. Planteamos el problema: Resolver el sistema de ecuaciones: $$\begin{cases} x - 2y - 6 = 0 \\ \frac{x - y}{2} + x = 4 \end{cases}$$

1. **State the problem:** We are given a system of two equations: $$x - 2y - 6 = 0$$

1. **State the problem:** Solve the system of equations by graphing: $$\begin{cases} y = 2x - 1 \\ y = -x + 5 \end{cases}$$

1. **State the problem:** We are given two linear equations:

1. El problema es factorizar el polinomio $$x^3 - 2x^2 - 5x + 6$$. 2. Para factorizar un polinomio cúbico, primero buscamos raíces racionales posibles usando el teorema del factor:

1. El problema es factorizar el polinomio $$x^3 - 2x^2 - 5x + 6$$ y determinar cuál de las opciones dadas es correcta. 2. Para factorizar un polinomio cúbico, primero buscamos raíc

1. **State the problem:** Simplify the expression $24 \div 6 + 4 \times (3 + 6)$.\n\n2. **Recall order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication and d

1. **State the problem:** Simplify the expression $b^{3/5} \cdot b^{4/2}$ assuming all variables are positive. 2. **Recall the rule for multiplying powers with the same base:**

1. We are asked to simplify the expression $7 \log_4 \left(4^{2x+5}\right) - 10 \log (x+5)$. 2. Recall the logarithm power rule: $\log_b (a^c) = c \log_b a$. Also, $\log_b b = 1$.

1. **Problem Statement:** We are asked to find the lowest common denominator (LCD) for pairs of denominators and then compare fractions by converting them to equivalent fractions w

1. **State the problem:** Simplify the expression $37(-10) - 4(2 \times 4) - 77$. 2. **Recall the order of operations:** Perform multiplication and division before addition and sub

1. Reduce $\frac{36}{63}$ to lowest terms. Step 1: Find the greatest common divisor (GCD) of 36 and 63.

1. **State the problem:** Simplify the expression $j^{-13} \cdot j^{4} \cdot j^{6}$. 2. **Recall the rule for multiplying powers with the same base:**