🧮 algebra

1. **State the problem:** Simplify the expression $$-(3ab + b^2 - 5a^2 b) + (a^2 - 5ab + 2b^2) - (a^2 b - 3a^2 + b^2)$$. 2. **Remove parentheses carefully, applying signs:**

1. **State the problem:** Find the value of $x$ such that $$1000^4 = 10^x.$$\n\n2. **Rewrite the base 1000 in terms of 10:** Since $1000 = 10^3$, we can write $$1000^4 = (10^3)^4.$

1. **State the problem:** Solve the equation $6y + 11 = 3y + 5$ for $y$. 2. **Isolate the variable terms:** Subtract $3y$ from both sides to get all $y$ terms on one side.

1. The problem is to find the value of 26% as a decimal or fraction. 2. Percent means per hundred, so 26% means 26 out of 100.

1. Énonçons le problème : Calculer $-1,5 \times \left((-2,8)^2 - 9,2 + 3,6\right)$ et vérifier si le résultat est égal à 20,16. 2. Rappelons la formule et les règles importantes :

1. The problem is to make the right-hand side (rhs) equal to the left-hand side (lhs) of an equation. 2. To do this, we need to identify the equation and then manipulate one side t

1. **State the problem:** There are 36 cookies in total. The number of peanut butter cookies equals the sum of all other types. There are 4 more sugar cookies than chocolate chip c

1. **State the problem:** Find the slope of the line passing through the points $(-6, -12)$ and $(8, -14)$. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1,

1. **State the problem:** Given a point $(m,n)$ on the graph of $y = f(x)$, find the corresponding point on the graph of $y = f(x - 11) + 4$. 2. **Recall the transformation rules:*

1. **State the problem:** A company buys inkjet printers, LCD monitors, and memory chips. Total items bought: 41.

1. **State the problem:** We need to write a system of linear equations to represent the purchase of inkjet printers, LCD monitors, and memory chips.

1. **State the problem:** We are given the function $$f(x) = -2|x-7| + 8$$ and want to understand its behavior and graph. 2. **Recall the absolute value definition:** The absolute

1. The problem is to simplify the fraction $\frac{3}{4}$. 2. The fraction $\frac{3}{4}$ is already in its simplest form because 3 and 4 have no common factors other than 1.

1. **State the problem:** Simplify the expression $$\left(\frac{-4 a^4 b^5 c^0}{2 a^2 b^3 c^6}\right)^{-3}$$. 2. **Recall the rules:**

1. Stating the problem: Simplify the expression $$\frac{10 x^6}{4 y^2} \times \frac{-4 a^4 b^5 c^0}{2 a^2 b^3 c^6} \times (-3) \times 9^{-2}$$. 2. Recall the rules:

1. **Problem statement:** Jason observes that the amount of money donated each hour increases by 15 compared to the previous hour, starting with 40 in the first hour. We need to: a

1. **State the problem:** We need to find $n(A)$, the number of elements in the set $A = \{127, 128, 129, 130, \ldots, 141\}$. 2. **Recall the formula:** For a set of consecutive i

1. The problem involves solving and understanding the system of inequalities: $$y < -\frac{3}{2}x + 5$$

1. **State the problem:** We are given three functions: $f(x) = x^2$, $g(x) = 2x$, and $h(x) = x^2 - 2x$. We need to fill in the table of values for $f(x)$ and $g(x)$ at $x = -2, -

1. **Problem statement:** Find the condition for which the line $y=mx+c$ touches the ellipse $$\frac{x^2}{25} + \frac{y^2}{16} = 1.$$ Then find the equation of the tangents with sl

1. Vamos a empezar explicando cómo resolver ejercicios de álgebra básicos, que suelen ser muy comunes en los exámenes. 2. Un problema típico es resolver una ecuación lineal, por ej