🧮 algebra

1. **State the problem:** Solve the equation $$\frac{3x}{5} = 2x - 9$$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side. We can eliminate the

1. **State the problem:** Solve the equation $$\frac{3x}{5} = 2x - \frac{9}{5}$$ for $x$. 2. **Write down the equation:** $$\frac{3x}{5} = 2x - \frac{9}{5}$$

1. The problem involves understanding the relationship between the trunk diameter (in cm) and the age (in years) of two types of trees: Eastern hemlock and Giant redwood, as shown

1. **Stating the problem:** We want to simplify fractions, which means reducing a fraction to its simplest form where the numerator and denominator have no common factors other tha

1. نبدأ بكتابة المعادلة المعطاة: $$5x^2 - 5x = \frac{625}{1}$$ 2. نلاحظ أن المقام هو 1، إذن المعادلة تصبح: $$5x^2 - 5x = 625$$

1. The problem is to convert a recurring decimal into a fraction. 2. Let's consider the recurring decimal $x = 0.\overline{3}$, which means the digit 3 repeats indefinitely.

1. المشكلة: حل المعادلة. 2. أولاً، يجب تحديد نوع المعادلة (خطية، تربيعية، إلخ) لمعرفة الطريقة المناسبة للحل.

1. **Problem Statement:** Given the equation $\left(x + \frac{1}{x}\right)^2 = 5^2$, find the values of expressions involving powers of $x$ and $\frac{1}{x}$. 2. **Step 1: Expand t

1. **Stating the problem:** We are given the algebraic expression $4 + n$ and asked to evaluate it when $n = 2$. 2. **Understanding the expression:** The expression $4 + n$ means t

1. The problem is to understand the difference between an algebraic expression and an algebraic equation, and solve the equation given. 2. An algebraic expression is a combination

1. **State the problem:** Solve the linear equation $3x - 6 = 12x + 9$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performi

1. **Stating the problem:** Nanjala and Cherono start from Mwanzo towards Mwisho, which are 17 km apart. Nanjala walks at 9 km/h and starts 45 minutes before Cherono, who cycles at

1. **Тооцоолох асуудлыг тодорхойлно:** Тооцоолох илэрхийлэл нь $$8.4 \div \left(-\frac{2}{5} + 0.2\right)$$ байна.

1. **State the problem:** Solve the inequality $x - 8 > 1$ for $x$. 2. **Recall the rule:** To solve inequalities, you can add or subtract the same number on both sides without cha

1. **State the problem:** We have a rectangular parking lot enclosed by a fence of length 110 meters. The length of the parking lot is 5 meters more than its width. We need to find

1. **State the problem:** Rationalise the denominator of the expression $\frac{6}{\sqrt{10}}$ and simplify the result. 2. **Formula and rule:** To rationalise a denominator contain

1. **State the problem:** Expand and simplify the expression $$(2 - \sqrt{5})(1 - 3\sqrt{5})$$. 2. **Formula used:** Use the distributive property (FOIL method) to expand the produ

1. The previous question involved solving a quadratic equation or analyzing a function (assuming from context). 2. To join this with the previous question, we need to clarify the e

1. **State the problem:** Simplify the expression $$\frac{2}{f(x)} - \frac{5}{g(x)}$$ as a single fraction in terms of $x$. 2. **Formula and rules:** To subtract fractions, find a

1. **State the problem:** We are given two functions $f(x) = 3x - 4$ and $g(x) = 4x + 1$. We need to find: (a) $f(-2)$

1. The problem involves understanding and performing operations with fractions and decimals arranged in a matrix-like format. 2. We start by interpreting each value: fractions like