🧮 algebra

1. Planteamos el problema: Encontrar el valor de $b$ para que exista el límite $$\lim_{x \to -1} \frac{b(x^3 + 3x^2 - 2x - 3)}{x^2 + 3x + 2}.$$\n\n2. Observamos que el denominador

1. **State the problem:** Solve the equation $7x - 12 = 30$ for $x$. 2. **Write the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, w

1. **State the problem:** Solve the compound inequality $n + 2 \leq -5$ and $n + 6 \geq -6$. 2. **Understand the problem:** We need to find all values of $n$ that satisfy both ineq

1. **Stating the problem:** Solve the inequality $n + 2 \leq -5$ and $n + 6 \leq -6$ for $n$. 2. **First inequality:** $n + 2 \leq -5$

1. **State the problem:** We need to identify the independent and dependent variables in the context of Autumn's car gas usage, given the formula $$m = 25g$$ where $m$ is miles dri

1. **State the problem:** Solve the linear equation $4x + 9 = 25$ for $x$. 2. **Isolate the variable term:** Subtract 9 from both sides to get rid of the constant on the left.

1. **State the problem:** Simplify the expression $$(12 - 8)^2 \times 2 \div 8$$ step by step using the order of operations. 2. **Apply parentheses first:** Calculate inside the pa

1. **State the problem:** Solve the matrix equation $$2X + A = B$$ for matrix $$X$$, where $$A = \begin{bmatrix}0 & -9 \\ 2 & 6 \\ -3 & 5\end{bmatrix}$$ and $$B = \begin{bmatrix}2

1. **State the problem:** We are given a formula relating distance $d$ and time $t$ for Austin's driving: $$t = \frac{d}{60}$$

1. **Problem Statement:** Determine the key characteristics of a linear function with a negative slope passing through the origin. 2. **Parent Function:** The linear function is ge

1. **State the problem:** Solve the equation $\frac{x}{4} - 6 = 10$ for $x$. 2. **Add 6 to both sides:**

1. The problem is incomplete as it shows a fraction with numerator $x$ but no denominator. 2. To solve or simplify a fraction, both numerator and denominator must be specified.

1. **State the problem:** Solve the equation $5x = 40$ for $x$. 2. **Formula and rule:** To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is 5.

1. **State the problem:** Calculate the value of the expression $$(-45) - (-30)$$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterp

1. **State the problem:** Simplify the expression $$(4 - 5x)(1 - 2x)(3x + 2)$$ by multiplying the three binomials. 2. **Use the distributive property (FOIL for binomials) step-by-s

1. The problem is to solve the expression $9) (-99) - = 6 * 9$. Since the expression is unclear, we interpret it as $-99 - x = 6 \times 9$ where $x$ is unknown. 2. Calculate the ri

1. **State the problem:** Expand and simplify the expression $$(2x + 5)(x - 2)(3x + 4)$$. 2. **Recall the formula:** To multiply multiple binomials or polynomials, multiply two at

1. **State the problem:** Solve the linear equation $3x - 7 = 11$ for $x$. 2. **Add 7 to both sides:** To isolate the term with $x$, add 7 to both sides:

1. **Problem:** Factor the trinomial $n^2 - 8n + 15$ completely. 2. **Formula and rules:** For a quadratic trinomial $ax^2 + bx + c$ where $a=1$, factorization looks for two number

1. Problem 40 is not provided, so we will solve problem 44: Solve the inequality $$8 - 10 > -3$$. 2. Write the inequality: $$8 - 10 > -3$$.

1. **State the problem:** Solve the equation $2x + 5 = 17$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse operat