🧮 algebra

1. **State the problem:** We have a bag with green, red, and blue marbles. The number of marbles for each color is given by expressions involving $x$ and $y$: - Green: $4x - y + 3$

1. **Problem 1:** Solve the equation $4^3 = 4(2x + 3)$. - Calculate $4^3 = 64$.

1. **State the problem:** Simplify and solve the given expressions and equations step-by-step. 2. **Simplify the first expression:**

1. The problem is to plot the graph of a function. 2. Since no specific function was given, let's consider a general exponential function for demonstration: $$y = a^x$$ where $a >

1. **Problem Statement:** Solve for $x$ given the departments' workers and their total: Department K = $x + 2^1$, Department L = $x$, Department M = $x - 10$, and their sum is 40.

1. El problema es expandir la expresión $4(x-5)(x-2)$ usando la propiedad distributiva. 2. La propiedad distributiva dice que $a(b+c) = ab + ac$. Aquí la aplicaremos dos veces porq

1. **State the problem:** We have a parabolic curve representing the bridge arch given by the function $f(x) = px^2 + \frac{1}{4}x + 91$. The length of the base $AB$ is 144 m, and

1. **State the problem:** Solve the equation $$2^2 (-y + 1) = \frac{3}{4} y$$ for $y$. 2. **Rewrite the equation:** Since $2^2 = 4$, the equation becomes $$4(-y + 1) = \frac{3}{4}

1. **State the problem:** We need to find all vertical and horizontal asymptotes of the rational function $$f(x) = \frac{3x^2 - 6x - 9}{2x^2 + 7}$$. 2. **Vertical asymptotes:** The

1. **State the problem:** Solve the inequality $$-7k - 1 + 7k < 8 + 3k - 6$$. 2. **Simplify both sides:** On the left side, combine like terms:

1. **State the problem:** Solve the inequality $$c + 38 - 8 \geq -4$$ and represent the solution on a number line. 2. **Simplify the inequality:** Combine like terms on the left si

1. The problem is to understand the relationship or pattern between the numbers 4, 5, and 6. 2. Since no specific operation or question is given, let's consider these as consecutiv

1. **State the problem:** Solve the inequality $-3(c - 22) < 15$ and express the solution in inequality notation. 2. **Use the distributive property:** Multiply $-3$ by each term i

1. **State the problem:** Solve the absolute value equation $$| -4y - 6 | + 4 = 6$$. 2. **Isolate the absolute value:** Subtract 4 from both sides:

1. **State the problem:** Solve the linear equations given: Equation 1: $x + 7 = -14$

1. **State the problem:** Solve the linear equation $5x + 2y = 19$ for $y$ in terms of $x$. 2. **Formula and rules:** To express $y$ in terms of $x$, isolate $y$ on one side of the

1. **State the problem:** Solve the linear equation $$3x + 2y = 12$$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. T

1. **Problem Statement:** Solve the linear equation $ax + b = 0$ for $x$. 2. **Formula and Rules:** The general form of a linear equation in one variable is $ax + b = 0$, where $a$

1. **State the problem:** Calculate the total amount Bong'i has to pay for water usage based on the tariffs and quantities given, including 15% VAT.

1. **Stating the problem:** Calculate the total cost of a meal that costs 159.50 with an added 10% service charge. 2. **Formula used:** Total cost = Original cost + Service charge

1. **State the problem:** Simplify or analyze the expression $4x^2 + 11x + y - 1$. 2. **Identify the terms:** The expression contains quadratic term $4x^2$, linear term $11x$, a li