🧮 algebra

1. **State the problem:** We need to find the value of the question mark (?) in the equation $$? \div \frac{3}{5} = 8$$

1. **State the problem:** We need to find the difference between the fractions $\frac{7}{11}$ and $\frac{7}{15}$ and express the answer in simplest form. 2. **Formula and rules:**

1. The problem asks to find the sum of the integers from 1 to 10. 2. We use the formula for the sum of the first $n$ natural numbers: $$S = \frac{n(n+1)}{2}$$ where $n=10$.

1. **State the problem:** We need to order the given expressions from least to greatest. 2. **Evaluate each expression:**

1. **State the problem:** Solve the system of equations: $$9^x (27)^y = 1$$

1. **State the problem:** Simplify the expression $$\frac{x+8}{x^2+9x+20} + \frac{x+5}{x^2+7x+12}$$ ignoring restrictions on the variable. 2. **Factor the denominators:**

1. Masalah: Cari nilai $x$ dalam persamaan linear $3x + 5 = 20$.\n\n2. Formula yang digunakan: Untuk menyelesaikan persamaan linear, kita perlu mengasingkan $x$ di satu sisi persam

1. The problem involves understanding logarithmic relationships and solving for variables given certain logarithmic values. 2. We use the logarithm properties and linear equations.

1. **State the problem:** We are given the polynomial function $$f(x) = 2x^3 + x^2 - 18x - 9$$ and need to determine which of the statements A, B, C, or D is true. 2. **Recall the

1. **State the problem:** We need to determine which binomial among $x-6$, $x+2$, $x+4$, and $x-7$ is NOT a factor of the polynomial $$x^3 - 11x^2 + 16x + 84.$$\n\n2. **Recall the

1. **State the problem:** We are given that $x - 1$ is a factor of the polynomial $x^3 - kx + 2x$ and need to find the value of $k$. 2. **Recall the Factor Theorem:** If $x - a$ is

1. **State the problem:** Solve the equation $$11b - 17 = -3b + 39$$. 2. **Write down the formula and rules:** To solve for $b$, we need to isolate $b$ on one side of the equation

1. **Stating the problem:** We will learn about fractions, how to add, subtract, multiply, and divide them. 2. **What is a fraction?** A fraction represents a part of a whole and i

1. **State the problem:** Solve the equation $$18x + 7 - 14x + (-6x) - 10 = -13$$. 2. **Combine like terms on the left side:** Group the terms with $$x$$ and the constant terms sep

1. The problem is to understand and work with fractions. 2. A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denomi

1. **State the problem:** Solve the quadratic equation $x^2 + 4x + 3 = 0$. 2. **Formula and rules:** The quadratic equation is generally solved using the quadratic formula:

1. **State the problem:** Simplify the expression $3^{-3} \times 27^2 \times (9^4)^{-5}$. 2. **Rewrite all terms with the same base:** Note that $27 = 3^3$ and $9 = 3^2$. So rewrit

1. **State the problem:** We are given a triangle with three angles labeled $x^\circ$, $2x^\circ$, and $(x - 20)^\circ$. We need to write an equation that models the sum of these a

1. **Problem:** Determine the slope of the line passing through the points $(-4, 15)$ and $(2, 6)$. 2. **Formula:** The slope $m$ of a line passing through points $(x_1, y_1)$ and

1. **State the problem:** Solve the system of linear equations: $$2y + x = 3$$

1. **State the problem:** Solve the linear equation $2y + x = 3$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to get $y$ alone on one side of the equa