🧮 algebra

1. **State the problem:** Simplify the expression $ (2x+3) + (4x-5)(2x+3) + (4x-5) $. 2. **Recall the distributive property:** To simplify expressions with parentheses, multiply te

1. **Problem statement:** Solve for $x$ given the equation $\left(3^x\right)^2 = 7.5$. 2. **Rewrite the equation:** Using the power of a power rule, $\left(a^m\right)^n = a^{mn}$,

1. The problem is to understand the value of $n$ given as 42. 2. Here, $n$ is simply a variable representing a number, and it is stated that $n=42$.

1. **Stating the problem:** We need to multiply the fraction $\frac{3}{4}$ by several fractions: $\frac{2}{2}$, $\frac{6}{6}$, $\frac{3}{3}$, $\frac{4}{4}$, and $\frac{5}{5}$. We w

1. **Énoncé du problème :** Étudier la fonction $g$ définie par $g(x) = x^3 + x^2 + 3x - 1$. 2. **Dresser le tableau de variations (TV) de $g$ :**

1. **State the problem:** Determine if the equation $5(3-2x) = 5x - 2(8x-7)$ is an identity (true for all $x$) or not. 2. **Expand both sides:**

1. **State the problem:** We need to compare the fractions $\frac{6}{8}$, $\frac{6}{9}$, and $\frac{6}{10}$ by finding a common denominator (LCD) to easily compare their sizes.

1. **State the problem:** Solve the equation $$x^{5} - 9x^{5} + 14 = 0$$. 2. **Simplify the equation:** Combine like terms:

1. **State the problem:** Divide the polynomial $8x^2 - 45y^2 + 18xy$ by the binomial $2x - 3y$. 2. **Formula and approach:** Polynomial division can be done using long division or

1. **State the problem:** Solve the equation $$8x^4 - 3 = 2$$ for $x$. 2. **Rewrite the equation:** Add 3 to both sides to isolate the term with $x$:

1. **State the problem:** Solve the equation $$\frac{4}{x - 3} = 8$$ for $x$. 2. **Formula and rules:** To solve for $x$, we will isolate $x$ by first eliminating the denominator.

1. The problem is to arrange the given mathematical expressions from smallest to biggest. 2. Let's evaluate or understand each expression:

1. The problem asks why the fraction $\frac{10}{10}$ was used in the expression $\frac{2a}{3b}$ to find an equivalent fraction. 2. To find an equivalent fraction, we multiply the n

1. Let's start by understanding the problem: Why is 10 used to find an equivalent fraction? 2. When finding an equivalent fraction, we multiply or divide the numerator and denomina

1. **Stating the problem:** Simplify the expression $$\frac{2a}{3b} - \frac{4a}{5b} + \frac{5a}{2b}$$ and explain why 10 is used as the number to expand it. 2. **Formula and rules:

1. **State the problem:** Simplify the expression $$\frac{ab + 3b - 2a - 6}{(a + 3)b}$$. 2. **Identify the numerator and denominator:**

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: $$5x^2 - 5x = 625$$