🧮 algebra

1. **State the problem:** Solve the linear equation for $y$ given the equation $-5x + y = -7$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation b

1. The problem is to solve the inequality $$\frac{2}{x} \leq -1$$. 2. To solve this, we first note that $$x \neq 0$$ because division by zero is undefined.

1. **Problem statement:** Given points $A(2, -3)$ and $B(-4, 1)$, (a) calculate the length $AB$, and (b) find the equation of the line passing through $A$ and $B$. 2. **Length of s

1. **State the problem:** (a) Given that $$4^3 \times 16^{\frac{1}{4}} = 2^x$$, find the value of $$x$$.

1. **State the problem:** Solve the equation $\sqrt{4n} + 12 = n$ for $n$. 2. **Rewrite the square root:** Note that $\sqrt{4n} = \sqrt{4} \cdot \sqrt{n} = 2\sqrt{n}$.

1. Das Problem: Wir wollen herausfinden, welche gebrochene rationale Funktion zu dem Bild passt, das eine Hyperbel zeigt mit einem senkrechten Asymptoten bei $x=2$ und einem waager

1. **State the problem:** Solve the linear equation $$4 - 3(x + 1) = 2x - 4$$. 2. **Use the distributive property:** Expand terms with parentheses.

1. **State the problem:** Solve the equation $2x - 6 = 4x + 2$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing the s

1. The problem is to evaluate the expression $\frac{(26.7 - 13 \frac{1}{5})}{1.8} + 0.125$. 2. First, convert the mixed number $13 \frac{1}{5}$ to an improper fraction or decimal:

1. El problema es factorizar el polinomio $$8x^3 - x - 5$$. 2. Para factorizar un polinomio cúbico, podemos intentar encontrar una raíz racional usando el teorema del residuo y lue

1. El problema es factorizar el polinomio $$x^2 + x + 1$$. 2. Para factorizar un trinomio cuadrático de la forma $$ax^2 + bx + c$$, buscamos dos números que multiplicados den $$ac$

1. **State the problem:** We are given the quadratic expression $x^2 + x + 1$ and want to analyze or simplify it. 2. **Formula and rules:** A quadratic expression is generally of t

1. **State the problem:** Simplify the expression $2 + x + 1$. 2. **Combine like terms:** The terms $2$ and $1$ are constants and can be added together.

1. **State the problem:** Solve the inequality $$-15x \leq 2x^2 + 18$$. 2. **Rewrite the inequality:** Move all terms to one side to set the inequality to zero:

1. **State the problem:** Simplify or factor the quadratic expression $6x^2 - 13x - 5$. 2. **Formula and rules:** To factor a quadratic $ax^2 + bx + c$, find two numbers that multi

1. **State the problem:** Simplify or analyze the quadratic expression $x^2 - 13x - 5$. 2. **Formula and rules:** The quadratic expression is in the form $ax^2 + bx + c$ where $a=1

1. **Stating the problem:** We are given the linear function $$y = 18 - 4x$$ and asked to find the value of $$y$$ when $$x = \frac{48}{13}$$. 2. **Formula used:** The function is a

1. **State the problem:** Solve the equation $95 - x = 69$ for $x$. 2. **Formula and rules:** To isolate $x$, we use the rule of adding or subtracting the same number on both sides

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 11$ nach $x$ auf. 2. Die verwendete Formel ist die Umkehrung der Addition und Multiplikation, um $x$ zu isolieren. Wichtig ist,

1. **State the problem:** We are given the absolute value function $$f(x) = |x + 3|$$ and need to express it as a piecewise function. 2. **Recall the definition of absolute value:*

1. **State the problem:** We want to find a system of inequalities that models the minimum population $P$ (in thousands) of crickets over time $t$ (in months). 2. **Understand the