🧮 algebra

1. Тэнцэтгэл бишийг уншиж ойлгоё: $|5x - 3| < 7$. 2. Модулын тэнцэтгэл бишийг задлахдаа доторх илэрхийлэл нь $-7 < 5x - 3 < 7$ гэж бичигдэнэ.

1. Problem: Given that 3 out of every 100 people are illiterate, find the number of illiterate people in a population of 1,500,000. 2. Formula: Use the proportion formula for ratio

1. Stating the problem: We are given the equation $$3(3y - 4x) + 4(5x - 6) = 2(4y - 9) - 13$$ and need to transform it into normal form and solve for the unknown $y$. 2. Expand bot

1. **Stating the problem:** We are given three terms of a sequence: $x - 1$, $2x$, and $4x - 3$. We need to find the value of $x$ such that these terms form an arithmetic progressi

1. Diberikan barisan aritmatika dengan suku pertama $a_1 = \frac{4}{3}$ dan suku kedua $a_2 = \frac{5}{3}$. Kita diminta mencari banyak suku $n$ sehingga suku ke-$n$ adalah 5. 2. R

1. **Problem Statement:** Find the shortest distance between two parallel lines given in the slope-intercept form $y=mx+c$. 2. **Formula and Explanation:** The shortest distance $d

1. **Problem Statement:** Find the equation of the circle that passes through the points of intersection of the two given circles $$S_1: x^2 + y^2 + 2x + 3y - 7 = 0$$

1. The problem is to understand why $\frac{1}{0}$ is undefined. 2. Division by zero is undefined because division is the inverse operation of multiplication.

1. **Problem:** Find the domain of definition of the function $$f(x)=\frac{x^2 - x + 6}{2x - 8}$$. 2. **Formula and rules:** The domain of a rational function is all real numbers e

1. Let's start by understanding what a sequence is: a sequence is an ordered list of numbers following a specific pattern. 2. To formulate an equation for a sequence, we often look

1. **Problem statement:** We are given the population of Grayrock in 1960 as 10,000 and in 1970 as 12,000. We assume the population grows exponentially and want to estimate the pop

1. **Problem statement:** Find two possible values of $x$ such that the distance between the points $(-1, 13)$ and $(x, 9)$ is $\sqrt{65}$. 2. **Formula used:** The distance $d$ be

1. **State the problem:** Solve the equation $$3^x = 4x + 5$$ for $x$. 2. **Understand the functions:** The left side is an exponential function $y=3^x$, which grows rapidly as $x$

1. The user requested to "sketch it," but no specific function or equation was provided to sketch. 2. To assist effectively, please provide the function or equation you want to be

1. **Problem:** Find the equation of the parabola given the focus at (0, 2) and vertex at (0, 4). 2. **Formula and rules:** The vertex form of a parabola with vertical axis is $$ (

1. **State the problem:** Solve the equation $7b - 15 = 5b - 3$ for $b$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing the

1. **State the problem:** Solve the equation $20 - 6 + 4k = 2 - 2k$ for $k$. 2. **Simplify both sides:** Combine like terms on the left side.

1. **State the problem:** Solve the equation $12c - 4 = 14c - 10$ for $c$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing th

1. **Problem:** Examine the injectivity and surjectivity of the function $f: \mathbb{N} \to \mathbb{N}$ defined by $f(x) = x^2$. Determine if $f$ is bijective. 2. **Injectivity:**

1. **State the problem:** Solve the quadratic inequality $$2x^2 - 3x \leq 10$$ and analyze the graph of the quadratic function $$y = 2x^2 - 3x$$. 2. **Rewrite the inequality:** Mov

1. The problem is to create an inequality or expression without using the symbols $>$ or $<$. 2. One way to express inequalities without using $>$ or $<$ is to use other mathematic