🧮 algebra

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

1. **State the problem:** Evaluate the expression $$\frac{\sqrt{900 - \left(\frac{30}{14}\right)^2}}{13}$$. 2. **Recall the formula and rules:** The square root function is defined

1. The problem is to simplify the expression $$3\sqrt{6} - 6$$. 2. Recall that $$\sqrt{a}$$ means the square root of $$a$$, and it cannot be simplified further unless $$a$$ is a pe

1. **Stating the problem:** We are given the expression \(\frac{\frac{2x}{9}}{1 - 2x} \div (1 - x - 3)\) and asked to solve it or simplify it.

1. The problem asks to find the difference between the values obtained by rounding 4.82 to one significant figure and to one decimal place. 2. **Rounding to one significant figure:

1. **Stating the problem:** We need to find which number from the list rounds to the same value when rounded to one significant figure and when rounded to one decimal place. 2. **U

1. **State the problem:** We need to find which number among 0.1245, 0.0255, 0.255, and 0.1255 rounds differently when rounded to two significant figures versus when rounded to two