🧮 algebra

1. Write the problem: Convert $(\sqrt{10})^3$ to exponential form. 2. Recall that $\sqrt{10} = 10^{\frac{1}{2}}$.

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. The problem is to simplify the fraction $\frac{3}{47}$. 2. The formula for simplifying a fraction is to divide the numerator and denominator by their greatest common divisor (GC

1. The problem is to understand the equation $b = 5a - c$ and how the variables relate. 2. This is a linear equation where $b$ depends on $a$ and $c$.

1. **State the problem:** Solve the equation $$4x + 18 = 6x$$ for $$x$$. 2. **Write down the equation:** $$4x + 18 = 6x$$

1. **State the problem:** Solve the equation $$5 = x + 1 + 3x$$ for $$x$$. 2. **Combine like terms:** On the right side, combine $$x$$ and $$3x$$ to get $$4x$$.

1. **State the problem:** Solve the equation $$3x + 19 = 40$$ for $$x$$. 2. **Isolate the term with $$x$$:** Subtract 19 from both sides to get rid of the constant on the left.

1. **State the problem:** Solve the equation $$\frac{6x - 2}{2} = x + 9$$ for $x$. 2. **Use the formula and rules:** To solve for $x$, first eliminate the fraction by multiplying b

1. **State the problem:** Solve the equation $$5(3x - 2) = -55$$ for $$x$$. 2. **Use the distributive property:** Multiply 5 by each term inside the parentheses.

1. **State the problem:** Solve the equation $$\frac{1}{2}(x - 3) = 24$$ for $$x$$. 2. **Understand the operations:** The equation represents two operations applied to $$x$$: first

1. **State the problem:** Solve the equation $$\frac{2x + 4}{5} = 12$$ for $x$. 2. **Understand the formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the

1. **State the problem:** We are given the linear equation $y = 6x + 11$ and want to understand its properties. 2. **Formula and explanation:** This is a linear function of the for

1. **State the problem:** We are given the equation $\frac{y}{x} = 2$ and need to understand or solve it. 2. **Understand the equation:** The equation $\frac{y}{x} = 2$ means that

1. The problem is to verify or understand the expression $x = \frac{y}{2}$. 2. This expression means that $x$ is half of $y$.

1. **State the problem:** Solve the equation $\frac{y}{x} = 2$ for $y$ in terms of $x$. 2. **Formula and rules:** The equation shows a ratio of $y$ to $x$. To isolate $y$, multiply

1. **State the problem:** Solve the equation $\frac{y}{x} = 2$ for $y$ in terms of $x$. 2. **Formula and rules:** The equation shows a ratio of $y$ to $x$ equal to 2. To isolate $y

1. **State the problem:** We are given the equation $n = 5ax$ and want to understand or manipulate it.

1. The problem asks: How much will the purchaser spend buying the printer and 6 ink cartridges? 2. The linear function given is $y = 25x + 40$, where $y$ represents the total cost

1. **State the problem:** Solve the system of linear equations: $$-2x + 3y = 14$$

1. **بيان المسألة:** لدينا المتتالية المعرفة بالعلاقة $u_{n+1} = \frac{3u_n + 2}{2 + u_n}$ مع $u_0 = \frac{3}{2}$. المطلوب: أ) إثبات أن $u_{n+1} = 3 - \frac{4}{2 + u_n}$ لكل $n \in

1. **State the problem:** Solve the inequality $$(\sqrt{x} + 2)^2 < (5 - \sqrt{x})^2$$. 2. **Recall the formula:** For any real numbers $a$ and $b$, $a^2 < b^2$ implies either $a <