🧮 algebra

1. **State the problem:** Solve the equation $$\frac{1}{2} + \frac{2}{3} = \frac{1}{x}$$ and find any non-permissible values for $x$. 2. **Identify non-permissible values:** Since

1. **State the problem:** Solve the inequality $2x^2 + 7x - 4 > 0$. 2. **Formula and rules:** To solve a quadratic inequality, first find the roots of the quadratic equation $2x^2

1. **State the problem:** Solve algebraically for $x$ in the equation $$6^{3x+1} = 2^{2x-3}.$$\n\n2. **Recall the formula and rules:** To solve equations with different bases, take

1. **State the problem:** Simplify the expression $$\log_m \sqrt{a} + 4 \log_m (m^4 a) - 2$$ into a single logarithm of the form $$\log_m (a^x m^y)$$ and find the values of $x$ and

1. **Stel het probleem vast:** We hebben een hoeveelheid jodium-131 die de toegestane hoeveelheid met een factor 10 overschrijdt.

1. We hebben een functie $f$ waarvan de grafiek een logaritmische functie is, gegeven door het punt $\left(\frac{25}{4}, 2\right)$. We zoeken het voorschrift van de vorm $y = \log_

1. The problem asks to find the inequality that determines the domain of the function $f(x) = \sqrt{\frac{1}{2}x - 10} + 3$. 2. The domain of a function with a square root requires

1. **State the problem:** Find the inverse of the equation $$5y + 4 = (x + 3)^2 + \frac{1}{2}$$. 2. **Rewrite the equation:**

1. **State the problem:** Marius earns interest each year following the sequence 200, 208, 216.30, 225, ... and we want to find the total interest earned by the 30th year. 2. **Ide

1. **State the problem:** We need to solve the equation

1. Let's start by stating the problem: How to factor an algebraic expression. 2. Factoring means rewriting an expression as a product of simpler expressions.

1. The problem asks to find the result of the expression $$\frac{7}{9} - \frac{3}{9}$$. 2. Since the denominators are the same, we can subtract the numerators directly: $$\frac{7}{

1. **State the problem:** Simplify the expression $9x^2(5-\sqrt{x})$. 2. **Recall the distributive property:** To simplify expressions like this, multiply $9x^2$ by each term insid

1. **Problem:** Solve the equation $7 - (4x - 5) = 18$. 2. **Formula and rules:** To solve linear equations, first simplify both sides by removing parentheses and combining like te

1. **Énoncé du problème** : Montrer que la fonction carrée $f(x) = x^2$ est croissante sur $[0; +\infty[$ et décroissante sur $]-\infty; 0]$. 2. **Définition d'une fonction croissa

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **State the problem:** We are given the cost function $C(x) = 0.5x^2 + 50x + 100$ and the revenue function $R(x) = 80x - 0.01x^2$. We need to find the profit function $P(x)$, th

1. **State the problem:** Solve the equation $$\sqrt{x} + 2 = 8$$ and check the solution. 2. **Isolate the square root term:** Subtract 2 from both sides:

1. **Problem statement:** A competitor runs a 20 km race. - First 4 km at 6 minutes per km.

1. **Planteamiento del problema:** Resuelve la ecuación $$-5(2 - x) + 3(2x + 4) = 5(4x - 2)$$ 2. **Fórmulas y reglas:** Para resolver ecuaciones lineales, aplicamos la propiedad di

1. **State the problem:** Greg rows at 2 1/2 miles per hour in still water. It takes the same time to row 3 miles upstream and 4 1/2 miles downstream. We need to find the rate of t