🧮 algebra

1. **State the problem:** Solve the equation $$3(2x+1)^2 = 2(52+1)$$ for $x$. 2. **Simplify the right side:** Calculate $52+1$.

1. **State the problem:** Solve the equation $$3(2x+1)^2 = 2(5x+1)$$ for $x$. 2. **Use the formula and rules:** Expand the squared term and simplify both sides.

1. **State the problem:** Graph the parabola given by the equation $$y = -x^2 + 2x + 8$$ and plot 5 points including the roots and the vertex. 2. **Formula and rules:** The equatio

1. **State the problem:** Solve the inequality $$\frac{3x^2}{5} + \frac{x}{4} - (x - 2) - \frac{1}{2}\left(x - \frac{1}{2}\right) \geq \left(\frac{x - 1}{2}\right)^2 + \frac{3x}{5}

1. **State the problem:** We need to graph the quadratic function $$y = 3x^2$$ and understand its properties. 2. **Formula and rules:** The general form of a quadratic function is

1. **State the problem:** Solve the inequality $$\left(-x - \frac{1}{3}\right)^2 + (3x + 1)^2 - \frac{x}{2} + \frac{1}{6} \geq 10x(x - 1) - \frac{37}{9}.$$\n\n2. **Expand the squar

1. **State the problem:** Simplify the expression $$\frac{2x}{x^2 - 3x - 88} - \frac{2x - 1}{x^2 - 10x - 11}$$. 2. **Factor the denominators:**

1. **State the problem:** Solve the inequality $$ (7x - 2)^2 - 7(x - \frac{2}{7})(7x + 1) + \frac{x}{2} > 3(7x - 2) + \frac{1}{7} $$ with the condition $$ x < \frac{2}{7} $$. 2. **

1. **State the problem:** Find the horizontal asymptote, removable and non-removable restrictions, and simplified factored form of the rational function $$y = \frac{x^3 + 4x^2 - 4x

1. The problem is to analyze and understand the graph of the rational function $$y = \frac{3}{x - 4} - 6$$. 2. The general form of a rational function with a vertical asymptote is

1. **State the problem:** Determine which of the given functions are one-to-one functions. 2. **Recall the definition:** A function $f$ is one-to-one (injective) if for every $a$ a

1. **Problem Statement:** Determine which of the given functions are one-to-one functions. 2. **Recall:** A function is one-to-one (injective) if each output corresponds to exactly

1. **State the problem:** Mr. Wells has two copiers. The first copier makes 1,000 copies in 30 minutes, and the second copier makes 1,000 copies in 20 minutes. We want to find how

1. **Problem:** Clayton can sweep the gym floor in 24 minutes, and Morgan can do it in 40 minutes. How long will it take if they work together? 2. **Formula:** When two people work

1. **State the problem:** Simplify or factor the quadratic expression $x^2 + 4x + 4$. 2. **Recall the formula:** A quadratic expression $ax^2 + bx + c$ can be factored using the fo

1. **State the problem:** An element with an initial mass of 640 grams decays by 27.5% per minute. We want to find how much of the element remains after 5 minutes, rounded to the n

1. **State the problem:** We need to find the value of a car after 11 years if it depreciates at 9.5% per year from an initial value of 20300. 2. **Formula used:** The value after

1. Let's clarify the question: "Why do we ignore the 2 in the division?" This usually happens when simplifying fractions or expressions where a factor cancels out. 2. Consider an e

1. **Stating the problem:** We are given the equation $35,45 = 26,497 + A_2 \times 24,72\%$ and need to solve for $A_2$. 2. **Rewrite the equation:** Convert the percentage to deci

1. **State the problem:** Solve the equation $$\sqrt{4x+36}+2=10$$ for $x$. 2. **Isolate the square root term:** Subtract 2 from both sides:

1. **State the problem:** Solve the equation $$\sqrt{5x-34} - 17 = -16$$. 2. **Isolate the square root term:** Add 17 to both sides to isolate the square root.