🧮 algebra

1. The problem is to subtract the fractions $\frac{9}{10}$ and $\frac{1}{2}$. 2. To subtract fractions, they must have a common denominator. The denominators here are 10 and 2.

1. The user asks if their simplification is correct, but no specific expression or problem is provided. 2. To verify simplification, one must provide the original expression and th

1. **State the problem:** Simplify the expression $\frac{7}{10} - \left(-\frac{1}{2}\right)$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positi

1. **State the problem:** Find the slope $m$ of the line passing through points $(1,7)$ and $(2,10)$. 2. **Formula:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where

1. **Problema:** Encontrar a função volume $V(x)$ de uma caixa feita a partir de um retângulo de papelão, onde $x$ é o tamanho do recorte quadrado nas extremidades. 2. **Fórmula us

1. **State the problem:** We need to evaluate the function $f(x) = -3x + 3$ at $x = 2$. 2. **Formula used:** The function is given by $f(x) = -3x + 3$. To find $f(2)$, substitute $

1. The problem is to simplify the expression $\frac{7}{10} - \left(-\frac{1}{2}\right)$.\n\n2. Recall that subtracting a negative number is the same as adding its positive counterp

1. The problem is to subtract the fractions $-\frac{3}{5}$ and $\frac{4}{5}$. 2. Since both fractions have the same denominator, we can subtract the numerators directly:

1. **State the problem:** Solve the absolute value inequality $$6|x - 8| \leq 12$$ and find the values of $x$ that satisfy it. 2. **Recall the rule for absolute value inequalities:

1. **Stating the problem:** We want to learn how to add and subtract positive and negative fractions. 2. **Formula and rules:** To add or subtract fractions, first find a common de

1. **State the problem:** Solve the absolute value equation $$3|x - 4| = 33$$ for $x$. 2. **Isolate the absolute value:** Divide both sides by 3 to get $$|x - 4| = \frac{33}{3} = 1

1. **Stating the problem:** A flower-girl buys roses at the rate of 4 rupees for 5 roses and sells them at 5 rupees for 4 roses. We need to find her profit percent. 2. **Understand

1. **State the problem:** Solve the fractional equation $$\frac{2x}{x-3} + \frac{4}{x+2} = \frac{10}{x^2 - x - 6}$$. 2. **Factor the denominator on the right side:** Note that $$x^

1. **Problem Statement:** Given a geometric progression (GP) with the first term $a_1 = 108$ and the fifth term $a_5 = \frac{4}{3}$, find:

1. **Сформулюємо задачу:** Довести тотожність $$\left( \frac{3}{y+3} + \frac{y^2 + 9}{y^2 - 9} - \frac{3}{3-y} \right) \cdot \frac{y+3}{y^2 + 6y + 9} = \frac{1}{y-3}.$$

1. **State the problem:** Simplify the expression $$\frac{3\sqrt{2} - 2\sqrt{3}i}{3\sqrt{2} + 2\sqrt{3}i}$$ where $i$ is the imaginary unit. 2. **Formula and rule:** To simplify a

1. **Stating the problem:** Prove that

1. Problema: Turime tris iš eilės einančius aritmetinės progresijos narius: $k - 2$, $5k - 1$, $8 + 3k$. Reikia rasti $k$ reikšmę. 2. Aritmetinės progresijos savybė: skirtumas tarp

1. **Énoncé du problème :** Montrer que pour tout $x \in \mathbb{R} \setminus \{1\}$, on a $f(x) > 1$ où

1. **Problem statement:** A wholesaler buys a watch for 12000 excluding VAT and sells it to a retailer for 16950 including VAT. The VAT rate is 13%. We need to find how much the re

1. Énoncé du problème : Résoudre l'inéquation $$f(x) - g(x) < 0$$ avec $$f(x) = - \frac{5x - 23}{x - 4}$$ et $$g(x) = \frac{3}{8} \sqrt{|x - 4|} - 5$$. 2. Formule et règles importa