🧮 algebra

1. The problem asks to find the absolute value of the number represented by the point on the number line. 2. The absolute value of a number is its distance from zero on the number

1. **State the problem:** Solve the inequality $\log x > \log (x-1)$. 2. **Recall the properties of logarithms:** The logarithm function $\log x$ is increasing for $x > 0$. This me

1. **State the problem:** Solve the equation $$-6 \log_{3}(x-3) = -24$$ for $x$. 2. **Isolate the logarithm:** Divide both sides by $-6$ to isolate the logarithmic term.

1. The problem asks us to find the expression when the base of the logarithm is changed to 3. 2. Recall the change of base formula for logarithms: $$\log_b a = \frac{\log_c a}{\log

1. **State the problem:** Solve the equation $-6 \log_{10} (3(x-3)) = -24$ for $x$. 2. **Isolate the logarithm:** Divide both sides by $-6$ to isolate the logarithmic expression.

1. **State the problem:** Solve for $x$ in the equation $\log_{10}(x) - \log_{10}(2) = 1$. 2. **Recall the logarithm subtraction rule:** $\log_b(a) - \log_b(c) = \log_b\left(\frac{

1. **Stating the problem:** We have the equation $$5(3x - 2) = ax + b$$ where $a$ and $b$ are constants. We want to find:

1. **State the problem:** Simplify the expression $$(2x^5 - 5x^2 + 3) + (5x^3 + 5x^2)$$. 2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have the

1. **Problem statement:** Solve the linear systems using the substitution method for g) and h). 2. **Recall substitution method:** Solve one equation for one variable, then substit

1. The problem asks to find an equivalent representation of the sum of two polynomials: $$(x^2 + 3x - 8) + (2x^2 - x + 9).$$ 2. To add polynomials, combine like terms. Like terms h

1. **Problem statement:** We are asked to perform a Kurvendiskussion (curve discussion) for the function $$f(x) = (x - 1) \cdot (x + 2)^2$$ starting with expanding (Ausklammern) th

1. Il problema chiede di utilizzare il teorema del resto per trovare il resto della divisione di un polinomio per un binomio del tipo $x - a$. 2. Il teorema del resto afferma che i

1. **State the problem:** We are given two functions: $$A(x) = x^3 - 2x^2 - 11$$

1. **Problem statement:** (a) Determine the temperature shown on the thermometer.

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by th

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by th

1. **Problemstellung:** Zeichne die Graphen der linearen Funktionen $f$, $g$ und $h$ aus Aufgabe 9a) in dasselbe Koordinatensystem. Gegeben sind:

1. **Problemstellung:** Gegeben ist die lineare Funktion $f(x) = 0{,}4x + 1$. Wir sollen den Graphen zeichnen und den Schnittpunkt mit der y-Achse bestimmen. 2. **Formel und wichti

1. **Problem:** Given the parametric form of a plane $E$, find its coordinate form (Cartesian equation). 2. **Formula and rules:**

1. **State the problem:** Find six numbers whose mean is 3 and range is 0. 2. **Recall the formulas:**

1. **State the problem:** Find six numbers whose mean is 3 and range is 6. 2. **Recall the formulas:**