🧮 algebra

1. Stating the problem: Solve the equation $$\frac{x+5}{4} = \frac{(5-3x)2 + 4}{5}$$ for $x$. 2. Simplify the right side numerator: $$(5-3x)2 + 4 = 2(5-3x) + 4 = 10 - 6x + 4 = 14 -

1. Stating the problem: Solve the equation $x + \frac{5}{4} = \frac{(5 - 3x)2 + 4}{5}$ for $x$. 2. Simplify the right side numerator: $(5 - 3x)2 + 4 = 2(5 - 3x) + 4 = 10 - 6x + 4 =

1. **State the problem:** Expand and fully simplify the expression $$(2x + 5)(4x - 3)(5x - 4)$$ to write it in the form $$ax^3 + bx^2 + cx + d$$ and find the values of $$a, b, c,$$

1. **State the problem:** Determine if the point $(3, -1)$ satisfies the system of inequalities represented by the shaded regions on the graph. 2. **Identify the lines and inequali

1. The problem asks if the point $(-4,4)$ satisfies the system of inequalities represented by two lines: - A blue line with an upward slope, shading above it.

1. **State the problem:** Determine if the point $(-2, -3)$ satisfies the system of inequalities represented by the two lines and their shaded regions. 2. **Identify the inequaliti

1. **State the problem:** We need to determine if the point $(-1,7)$ satisfies the system of inequalities: $$2x + 5y > -6$$

1. The problem asks if the point $(1, 5)$ is a solution to the system of inequalities represented by the graph. 2. The graph has two boundary lines:

1. **State the problem:** We need to solve the system of inequalities graphically:

1. The problem is to simplify the expression $\log 3 - \log 4$. 2. Recall the logarithm property: $\log a - \log b = \log \left( \frac{a}{b} \right)$.

1. The problem is to simplify the expression $\sqrt{2}$.\n\n2. The square root of 2, written as $\sqrt{2}$, is an irrational number and cannot be simplified further into a simpler

1. **تمرين 1: إنشاء الأعداد على المستقيم العددية** - الأعداد المعطاة: $\frac{3}{4}, \frac{6}{7}, \frac{2}{6}, \frac{1}{6}$.

1. **Rendre le dénominateur un nombre entier** Pour chaque fraction avec un dénominateur décimal, multiplier numérateur et dénominateur par une puissance de 10 pour éliminer la vir

1. **State the problem:** Harriet bought $t$ meters of fabric. James bought 8 times as much fabric as Harriet, so James initially had $8t$ meters. 2. James returned 63 meters of fa

1. **State the problem:** We have $m$ kg of cheese.

1. **State the problem:** When 14 is subtracted from half of the number $k$, the result is at most 18. 2. **Translate the problem into an inequality:** Half of the number $k$ is $\

1. **State the problem:** We have three vegetable patches with areas:

1. Das Problem: Wir betrachten die Verkäufe eines Hauses und wollen verstehen, wie man diese mathematisch darstellen oder analysieren kann. 2. Zunächst definieren wir eine Variable

1. Das Problem ist, ein Beispiel mit den gegebenen Formeln zu berechnen. Da keine spezifischen Formeln oder Werte angegeben sind, werde ich ein allgemeines Beispiel mit einer typis

1. Problem a: Find how many times as high Mount Everest is compared to the tallest tree Hyperion. Given:

1. **Stating the problem:** We are given two relations: - $y = 30 - 2x$