🧮 algebra

1. **State the problem:** Solve the inequality $$\frac{x-9}{3} - \frac{x+1}{2} < \frac{5x}{6}$$. 2. **Find a common denominator:** The denominators are 3, 2, and 6. The least commo

1. **State the problem:** We have a piecewise function $$f(x) = \begin{cases} x - a, & x < 0 \\ a x^2 + b x + 1, & 0 \leq x \leq 1 \\ x^2 + 2x, & x > 1 \end{cases}$$

1. **State the problem:** Solve the inequality $4x(x) - 25 + 3(x-1) > 4x(x-4) + 15$. 2. **Rewrite the inequality:**

1. **State the problem:** We need to find the value of $b$ such that the slope of the line passing through the points $(-2, 3)$ and $(4, b)$ is 12. 2. **Recall the slope formula:**

1. **Problem statement:** Find the difference between the two expressions:

1. **State the problem:** Determine the domain and range of the function $f(x)$ based on the given graph description. 2. **Recall definitions:**

1. Problém: Najděte druhou absolutní hodnotu výrazu $|2x-1|$. 2. Vzorec: Absolutní hodnota $|a|$ je definována jako $a$, pokud $a \geq 0$, a $-a$, pokud $a < 0$.

1. Stated problem: Vyřešíme rovnici $$|x - 4| + |2x - 7| = |x| + 3$$ pomocí nulových bodů. 2. Nulové body absolutních hodnot jsou body, kde se výraz uvnitř absolutní hodnoty rovná

1. **Enunțul problemei:** Avem o lege de compoziție definită prin $$x * y = \sqrt{(x^2 + 2)(y^2 + 2)} + m,$$

1. **State the problem:** Find two numbers that multiply to 108 and add to -31. 2. **Formula and rules:** Let the two numbers be $x$ and $y$. Then:

1. **Stating the problem:** We have a laptop shop selling two types of laptops: budget and premium.

1. Problem 9: Calculate the percentage of votes and pie chart angles for each sport. Total students = 120

1. Planteamos el problema: calcular la expresión $$-2 - (-4 + 2) + (-5 + 1) - [(+7 - 8) - (+1 - 4)] - \{ -[-(+3 - 5)] \}$$ usando la ley de signos. 2. Recordemos la ley de signos p

1. **State the problem:** Solve the equation $60x = -36$ for $x$. 2. **Formula and rule:** To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is 6

1. **State the problem:** Solve the equation $$\frac{x^*}{0.2} = 3.2$$ for $x^*$. 2. **Formula and rules:** To isolate $x^*$, multiply both sides of the equation by $0.2$ to cancel

1. State the problem: Solve the inequality $|2n-18|\le 2$.\n\n2. Use the absolute value rule (two cases): Since $|A|\le b$ with $b\ge 0$, we can write it as an AND of two inequalit

1. State the problem: Express each statement using an inequality involving absolute value. 2. Use the absolute value modeling rule:

1. **Problem 4:** Calculate the total weekly earnings $f(x)$ for $x=40$ and $x=60$ deliveries using the piecewise function: $$f(x) = \begin{cases} 12x, & 0 \leq x \leq 50 \\ 18 (x

1. Problema: Determine si el conjunto es una función y su dominio para (a) \(y = \sqrt{x^2 - 4}\).\n\n2. Fórmula y reglas: Para que \(y = \sqrt{f(x)}\) sea real, el radicando debe

1. **Problem 12:** Five balls with values 10, 5, 7, 13, and 20 move simultaneously in directions indicated by arrows. When two balls moving in opposite directions collide, the bigg

1. The problem states that the curve $y=f(x)$ has a maximum point at $(2,3)$. 2. We need to find the maximum point of the curve $y=2f(x-1)$.