🧮 algebra

1. **State the problem:** Solve the equation $$\frac{1}{8} + c = \frac{4}{5}$$ for $c$. 2. **Isolate $c$:** To find $c$, subtract $\frac{1}{8}$ from both sides:

1. **State the problem:** Solve the equation with fractions and variable $x$: $$\frac{a}{b} x + \frac{c}{d} = \frac{e}{f} x + \frac{g}{h}$$

1. Das Problem lautet: Finde die Nullstellen der Funktion $$f(x) = 3(x - 3)(x - 7)$$. 2. Die Nullstellen einer Funktion sind die Werte von $x$, für die $f(x) = 0$ gilt.

1. **State the problem:** Solve the equation $$\sqrt{2x+2} = -2 + \sqrt{6x-6}$$. 2. **Important note:** The square root function $$\sqrt{y}$$ is defined only for $$y \geq 0$$ and a

1. The problem is to simplify the expression where the first square root covers $(2x+2)$ and the second square root covers $(6x-6)$. 2. The expression is $$\sqrt{2x+2} - \sqrt{6x-6

1. The problem is to simplify an expression where both square roots extend to the factor on the right. 2. Recall the property of square roots: $$\sqrt{a} \times \sqrt{b} = \sqrt{a

1. **State the problem:** Solve the equation $$\sqrt{2}x + 2 = -2 + \sqrt{6}x - 6$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to isolate the square root term

1. **State the problem:** Evaluate the expression $$\frac{(-3)(6)}{(2-5)^2}$$ step by step. 2. **Recall the order of operations:** Parentheses first, then exponents, multiplication

1. **State the problem:** Solve the system of equations graphically: $$2x = 8y$$. 2. **Rewrite the equation in slope-intercept form:** To graph the equation, express it as $$y = mx

1. **State the problem:** Combine the like terms in the expression $19e - 2 - 7e + 2 - 2e$. 2. **Identify like terms:** Like terms are terms that contain the same variable raised t

1. **State the problem:** Combine the like terms in the expression $4s + 12s - 3s - 8 - 12s$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to

1. Statement of the problem. Solve the equation $\frac{x}{4} = \frac{1}{2}$.

1. **Problem 1: Find the length of the enlarged copy given the original length is 15 cm.** Since no scale factor or additional information is given, we cannot determine the enlarge

1. Stating the problem: Solve the equation $$\frac{8}{10} = \frac{w}{5}$$ for $w$. 2. Use the cross-multiplication rule for proportions: $$a/b = c/d \implies ad = bc$$.

1. **State the problem:** Convert the mixed number $2 \frac{3}{5}$ to an improper fraction in its lowest terms. 2. **Recall the formula:** To convert a mixed number $a \frac{b}{c}$

1. **State the problem:** Simplify the expression consisting of three parts: $6a^3$, $\frac{5b}{21a}$, and $10b^2$. 2. **Analyze each part:**

1. **State the problem:** Simplify the expression $$\frac{18x^2}{x - 1} \div \frac{x}{2x - 2}$$. 2. **Rewrite the division as multiplication by the reciprocal:**

1. **State the problem:** Find the product of $\sqrt{66}$ and $\sqrt{15}$ in simplest radical form. 2. **Recall the property of square roots:** The product of square roots can be c

1. The problem involves understanding the coordinates transformation given by the point $(x+9, y-2)$. 2. This represents a translation of any point $(x,y)$ in the Cartesian plane b

1. **Stating the problem:** Vi ska hitta koordinaterna för punkten där linjerna A och B skär varandra.

1. **State the problem:** Find the secret three-digit number based on the clues given. 2. **List the clues:**