🧮 algebra

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and rules:** To solve a rational equation, multiply both sides by the denominator to eli

1. **Stating the problem:** We have a total sum of 6727 with 29 factors listed, some repeated and some decimal values. We need to divide these factors into two separate sums such t

1. Il problema chiede di risolvere l'espressione $$\left(\frac{9}{12} a^{2} b\right)^2$$. 2. La regola per elevare un prodotto a una potenza è elevare ogni fattore alla potenza: $$

1. **State the problem:** We are given the sequence 4, 7, 12, 19, 28, 39 and need to find a formula for the nth term, $a_n$. 2. **Analyze the sequence:** Calculate the differences

1. **State the problem:** Find a formula for the nth term $a_n$ of the sequence: 4, 7, 12, 19, 28, 39. 2. **Analyze the sequence:** Calculate the differences between consecutive te

1. **State the problem:** Simplify or understand the expression $$\left(\frac{a - 3}{a + 2}\right)^{1 - \sqrt{2}}$$. 2. **Recall the exponent rule:** For any base $x$ and exponents

1. **State the problem:** Simplify or analyze the expression $$\frac{(a - 3)^{1 - \sqrt{2}}}{a + 2}$$ where $a$ is a variable. 2. **Recall the rules:**

1. Das Problem lautet: Löse die Gleichung $$2x + 3 = 7$$. 2. Die allgemeine Formel zum Lösen linearer Gleichungen ist: $$ax + b = c \Rightarrow x = \frac{c - b}{a}$$.

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 3x + 2y + z = 2 \\ 7y + 2z = 4 \\ -10z = 6 \end{cases}$$

1. The problem is to find the domain of the function $f(x)$ given the table and graph description. 2. From the table, $f(x)$ is undefined for $x = -5, -4, -3, -2$ and defined start

1. **Problem statement:** Sketch the graph of the piecewise function

1. **State the problem:** Given the function $f(x) = 4\sqrt{x} + 3$, solve for $x$ when $f(x) = 10$. 2. **Set up the equation:**

1. The problem presents a table with two rows: the first row contains the numbers 1, 2, 3, and 4, and the second row contains the values 178.39, 213.86, 257.14, and 307.95 respecti

1. **State the problem:** Solve the quadratic equation $$c t^2 + 15t = -36$$ for $t$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **Stating the problem:** We are given a V-shaped graph centered at the origin with points extending to the left and right. We need to find the domain, range, highest point, and

1. **State the problem:** We are given a graph of a V-shaped figure and asked to determine the domain, range, whether it is a function or relation, and explain why.

1. The problem is to simplify the expression \( \frac{3x - 3y}{5x - 5y} \). 2. We start by factoring out the common factors in the numerator and denominator.

1. **Problem:** Simplify $2m^2 \cdot 2m^3$. 2. **Formula:** When multiplying powers with the same base, add the exponents: $a^x \cdot a^y = a^{x+y}$.

1. The user is asking if the function value after $x=5$ is $2$, specifically if $f(6) = 2$. 2. To clarify, if a function $f(x)$ is defined such that $f(5) = 2$, then the value at $

1. **State the problem:** Solve the linear equation $-3x + 3 = 4 - 3$ for $x$. 2. **Simplify the right side:**

1. **State the problem:** We need to graph the piecewise function: $$f(x) = \begin{cases} x - 3 & x < -1 \\ -x & -1 \leq x \leq 2 \\ -x - 1 & x > 2 \end{cases}$$