🧮 algebra

1. The problem is to solve the inequality disregarding those that are strictly greater than or less than $x$. 2. Since the user requests to disregard inequalities of the form $x >

1. **Problem Statement:** Simplify the expression $$\frac{\sqrt[3]{x^6 y^9}}{(x^{\frac{1}{2}} y^{\frac{1}{3}})^3} \cdot \sqrt{x^4 y^2}$$ where $x > 0$ and $y > 0$. 2. **Recall the

1. **Problem:** Solve the equation $2^{x+2} = 4\sqrt{8}$. 2. **Step 1:** Express all terms with the same base if possible.

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x + y - z = 8 \\ -3x - y + 2z = -11 \\ -2x + y + 2z = -3 \end{cases}$$

1. **State the problem:** Solve the equation $-0.2x = 1.6$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ by dividing both sides of the equation by the

1. **State the problem:** Find the sum of the arithmetic series starting with 25, 22, 19, ... up to the 22nd term. 2. **Identify the first term and common difference:** The first t

1. State the problem: Find the solution set for the equation $2x - 5 = 9$. 2. Use the formula: To solve for $x$, isolate $x$ by performing inverse operations.

1. **State the problem:** Find the sum of the first 35 terms of the geometric series: $$8, -12, 18, \ldots$$ 2. **Identify the first term and common ratio:** The first term is $$a

1. **State the problem:** Find the sum of the first 35 terms of the geometric series: $$8, -12, 18, \ldots$$ 2. **Identify the first term and common ratio:** The first term is $$a

1. The problem is to find the missing numbers in the last row of the matrix: $$\begin{matrix} 38 & 71 & 78 & 73 & 86 \\ 85 & 33 & 17 & 42 & 99 \\ 99 & 22 & 47 & 39 & 31 \\ 87 & 22

1. **State the problem:** Find the sum of the arithmetic series starting with 25, 22, 19, ... up to the 22nd term. 2. **Identify the series type and formula:** This is an arithmeti

1. The problem is to find the missing numbers in the last row of the given matrix: 38 71 78 73 86

1. **Problem Statement:** Solve the equation step by step. 2. **Step 1: Identify the equation.** Since the user did not specify an equation, let's assume a simple example: Solve fo

1. The problem is to find the 4th term of a sequence. 2. To find the 4th term, we need the formula or rule defining the sequence. Since it is not provided, let's assume a common ar

1. **State the problem:** We are given the arithmetic sequence defined by the formula $a(n) = -6 - 4(n - 1)$ and need to understand or find terms of this sequence. 2. **Formula exp

1. **State the problem:** We are given the arithmetic sequence defined by the formula $a(n) = -6 - 4(n - 1)$ and need to understand or find terms of this sequence. 2. **Formula use

1. The problem is to solve for $y$ in an equation involving $y$ (the exact equation is not provided, so we will consider a general approach). 2. To solve for $y$, isolate $y$ on on

1. The problem is to find the values of $y$ for given values of $x$: $-2.3$, $-2.2$, $-2.1$, $-1.9$, $-1.8$, and $-1.7$. 2. However, the function or equation relating $x$ and $y$ i

1. **State the problem:** We have a radioactive isotope with an initial amount of 1921 grams at year 0 and 1454 grams at year 2. The decay follows a geometric sequence, and we need

1. **Problem Statement:** We have a marching band forming rows with band members increasing by 2 each row, starting with 7 in the first row. We want to find a general formula for t

1. **State the problem:** We are given an arithmetic sequence defined by the formula $$a_n = 2 - 5(n - 1)$$ and need to find the first three terms $$a_1, a_2, a_3$$ and the common