🧮 algebra

1. **State the problem:** We need to find the value to replace the box (☐) in the equation $$7 + 3x - 1 = \boxed{\phantom{a}} (x + 2)$$ so that the equation has infinitely many sol

1. **State the problem:** Solve the equation $$\frac{3}{2} (2 - 6x) + 1 = 3 - 5x.$$\n\n2. **Use the distributive property:** Multiply $$\frac{3}{2}$$ by each term inside the parent

1. **State the problem:** Use the box method to distribute and simplify the product $$(-6x - 4)(-x^3 + 4x^2 - x + 6)$$. 2. **Recall the box method:** This method involves creating

1. The problem involves understanding the expression $n + 1$. 2. This is a simple algebraic expression where $n$ is a variable and $1$ is a constant.

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 3 to eliminate the d

1. **Stating the problem:** We have two fraction equations to solve for $x$:

1. **State the problem:** Simplify the expression $19.88^{-2022} \times 10^{2025}$. 2. **Recall the rules:** When multiplying powers with different bases, you cannot combine the ex

1. The problem is to evaluate the expression $5^3 + (15 + 9) - (2 + 14) \div 4 \cdot 2$. 2. The correct order of operations is parentheses, exponents, multiplication and division (

1. **State the problem:** Simplify the complex fraction $$\frac{-6 + i}{3 + 2i}$$. 2. **Formula and rule:** To simplify a fraction with complex numbers, multiply numerator and deno

1. **Problem Statement:** Graph the circle given by the equation $$ (x-3)^2 + (y+2)^2 = 16 $$. 2. **Formula and Explanation:** The general equation of a circle is $$ (x-h)^2 + (y-k

1. **State the problem:** We need to find the polynomial representing the area of the shaded region between a large square with side length $z+6$ and a smaller square inside it wit

1. **State the problem:** Solve the equation $$-12p = -78$$ for the variable $p$. 2. **Formula and rules:** To solve for $p$, we need to isolate $p$ on one side of the equation. Si

1. **State the problem:** Solve the equation $$\frac{1}{2} q = -24$$ for the variable $q$. 2. **Formula and rules:** To isolate $q$, multiply both sides of the equation by the reci

1. **State the problem:** Solve the linear equation $4x + y = 11$ for $y$ in terms of $x$. 2. **Formula and rules:** To express $y$ as a function of $x$, isolate $y$ on one side of

1. The problem asks to determine if the ordered pair (2, -2) is a solution to the system: $$\begin{cases} 3x + y = 4 \\ x - 3y = -4 \end{cases}$$

1. The problem provides a set of points with coordinates $(X, Y)$: $(-3, -5), (-2, -3), (-1, -1), (0, 1), (1, 3), (2, 5), (3, 7), (4, 9)$. We want to find the equation of the funct

1. The problem presents multiple equations, but per instructions, we will solve only the first one: $$y = \frac{x}{\sqrt{w_0}}$$. 2. This equation expresses $y$ as a function of $x

1. **State the problem:** We want to find the resulting exponent on $y$ in the expression $$\left(\frac{x^m}{y^n}\right)^a$$ when $m=7$, $n=6$, and $a=6$.

1. **State the problem:** Solve the linear equation $3k + 3 = 33 - 2k$ for $k$. 2. **Write down the equation:**

1. **State the problem:** Solve the linear equation $9x + 8 = 6x + 2$ for $x$. 2. **Write down the equation:**

1. **Stating the problem:** Find the next term in each sequence: a) 16, 25, 36, 49, ...