🧮 algebra

1. **State the problem:** We need to determine which points satisfy the inequality $$y \geq x^2 - 2x - 15$$. 2. **Recall the inequality:** For each point $(x,y)$, substitute $x$ an

1. **State the problem:** We need to analyze and graph the inequalities: 1) $y > 3x^2$

1. **State the problem:** Solve the cubic equation $$6x^3 + 2x^2 - 19x - 30 = 0$$. 2. **Formula and approach:** We will try to find rational roots using the Rational Root Theorem,

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula to solve linear equations is to isolate the variable on one side.

1. Solve $x^2 - 9x + 20 > 0$. Step 1: Factor the quadratic.

1. Solve $x^2 - 9x + 20 > 0$. - Factor the quadratic: $x^2 - 9x + 20 = (x - 4)(x - 5)$.

1. **Problem:** A square garden has an area of $$x^2 + 10x + 25$$ square meters. Find the side length by expressing the area as the product of two equal factors. 2. **Formula:** Th

1. **Problem statement:** (a) Find expressions equivalent to $$5x + 25$$ from the list: $$5(x + 5), 5\cdot x + 5\cdot 5, 5(5x + 1), 30x$$.

1. **State the problem:** We need to find which expressions are equivalent to the given algebraic expressions.

1. **Problema:** Resolver $\log_3 81 = x$ aplicando definición. La definición de logaritmo dice que $\log_a b = c$ es equivalente a $a^c = b$.

1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 13x + 42$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two number

1. **Problem Statement:** We are given two sequences and asked to extend each with three more terms.

1. **State the problem:** We are given the sequence $1, 8, 27, 64, \ldots$ and asked to describe the pattern. 2. **Identify the pattern:** Notice that each term looks like a cube o

1. **State the problem:** We are given the function $$f(x) = (x - 1) \cdot (x + 1) \cdot (x + 5)$$ and we want to simplify or expand it.

1. **State the problem:** Solve the inequality $$\frac{x^2 - x - 6}{x + 1} \leq 0$$ and represent the solution on a number line and in union notation. 2. **Factor the numerator:**

1. **State the problem:** Solve the inequality $$\frac{x^2 - 9}{x - 1} < 0$$ and find the solution set with its union and number line representation.

1. **State the problem:** Solve the inequality $$\frac{x^2 - 4}{x + 3} > 0$$ and express the solution as a union of intervals and on a number line. 2. **Rewrite the inequality:** N

1. **State the problem:** Solve the inequality $$x^2 - \frac{4}{x} + 3 > 0$$ and express the solution as a union of intervals and on a number line. 2. **Rewrite the inequality:** T

1. **State the problem:** Solve the inequality $$\frac{2x - 5}{x + 1} \geq 3$$. 2. **Rewrite the inequality:** Move all terms to one side to compare to zero:

1. **State the problem:** Simplify the expression $x - 2x$. 2. **Recall the rule:** When subtracting like terms, subtract their coefficients.

1. **State the problem:** Simplify the expression $x+3-(2x-4)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to each term inside th