🧮 algebra

1. Énoncé du problème : Résoudre dans $\mathbb{R}$ l'inéquation $$y(x) < -2x + 5.$$ 2. Pour résoudre une inéquation de la forme $$y(x) < f(x),$$ il faut trouver les valeurs de $x$

1. The problem asks: What is $c$? 2. To answer this, we need more context or an equation involving $c$.

1. Énoncé du problème : Résoudre dans $\mathbb{R}$ l'inéquation $$y(x) < -2x + 5$$. 2. Pour résoudre cette inéquation, il faut comprendre que $y(x)$ est une fonction dont on cherch

1. **Problem:** Solve the first pair of simultaneous equations: $$\frac{1}{2}x + \frac{2}{3}y = 6 \frac{1}{5}$$

1. **State the problem:** Simplify the expression $$\left(\frac{x^{\frac{4}{3}}}{-125 y^{-\frac{9}{3}} z^{\frac{8}{3}}}\right)^{-\frac{1}{3}}$$. 2. **Recall the power of a quotient

1. **State the problem:** Solve the equation $$\left(\frac{3}{7}\right)^{3x-7} = \left(\frac{7}{3}\right)^{7x-3}.$$\n\n2. **Rewrite the right side:** Note that $$\frac{7}{3} = \lef

1. **State the problem:** Simplify the expression $$\frac{(x + \sqrt{3})^2}{\sqrt{2} x^2 - 3\sqrt{2}} \cdot \frac{\sqrt{2}x - \sqrt{6}}{3}$$. 2. **Expand the numerator of the first

1. **Problem:** Factorize the expression $x^2 - x - 90$ using the AC method. 2. **Formula and rules:** The AC method involves multiplying the coefficient of $x^2$ (which is $1$) by

1. **State the problem:** We are given the function $f(x) = -x - 4$ and need to find the values of $f(x)$ for $x = -2, 4, 6, 4, 5$. 2. **Formula used:** The function is defined as

1. **State the problem:** Solve for $\alpha$ in the equation $$25 = 6\alpha + 7$$. 2. **Isolate the term with $\alpha$:** Subtract 7 from both sides:

1. **State the problem:** Find the domain and range of a function. Since the function is not specified, let's consider a general approach. 2. **Domain:** The domain of a function i

1. The problem is to analyze the function $f(x) = 1 + x^2$. 2. This is a quadratic function where the term $x^2$ dominates the shape.

1. **State the problem:** Expand the expression $$6a (5a - 8b - 1)$$. 2. **Formula used:** To expand, use the distributive property: $$x(y + z + w) = xy + xz + xw$$.

1. Намерете x, ако: а) $2^5 = x$

1. **State the problem:** Find the first three terms of the sequence defined by the nth term formula $a_n = 3n + 1$. 2. **Formula used:** The nth term of the sequence is given by $

1. **Problem statement:** Solve the equation $$x^2 = |2x + 4| + |x - 2|$$ for real values of $x$. 2. **Key idea:** Because of the absolute values, split the problem into intervals

1. **State the problem:** Solve the equation $8k - 19 = 3 + 16$ for $k$. 2. **Simplify the right side:**

1. **State the problem:** We need to find the numbers that go in the two red square boxes in the equation: $$2(\square - 4x) + \square(3x - 1) = 2(2x + 3)$$

1. **Problem statement:** Calculate the total net salary paid by company "A" in December based on the given employee data. 2. **Given data:**

1. **State the problem:** Solve the system of equations for $x$, $y$, and $z$: $$\begin{cases} x + y + 2x = 4 \\ x + y + 3x = 5 \\ 2x + y + z = 2 \end{cases}$$

1. **State the problem:** Solve the system of equations: $$\begin{cases} x + y + 2x = 4 \\ x + y + 3x = 5 \\ 2x + y + z = 2 \end{cases}$$