🧮 algebra

1. The problem asks to write the sentence "The difference of -42 and 8 is -50" as an equation. 2. "Difference" means subtraction, so we subtract 8 from -42.

1. **State the problem:** Solve the equation $$3(x + 5) = 12$$ for $$x$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. The problem asks to find the area of a square with side length $9x$ centimeters. 2. The formula for the area of a square is:

1. **State the problem:** We need to find the number $x$ such that four times the sum of the number plus 2 equals eight times the number minus 28. 2. **Write the equation:** The pr

1. **State the problem:** Solve the equation $$21 = 3x - 3$$ for $$x$$. 2. **Add 3 to both sides** to isolate the term with $$x$$:

1. **State the problem:** Evaluate the expression $$\frac{7x + 2}{2y}$$ when $$x = 4$$ and $$y = -5$$. 2. **Write the formula:** The expression is $$\frac{7x + 2}{2y}$$.

1. The problem asks if the number 12 is a solution to the equation $k - 9 = 3$. 2. To check, substitute $k = 12$ into the equation.

1. The problem states: "A number added to -11 amounts to -25." We need to write this as an equation using $x$ to represent the number. 2. The phrase "a number added to -11" transla

1. **State the problem:** We need to find a number such that six times the number plus 8 equals 32. 2. **Write the equation:** Let the number be $x$. The equation is:

1. **State the problem:** Solve the equation $$-1(t - 8) = 4$$. 2. **Apply the distributive property:** Multiply $$-1$$ by each term inside the parentheses.

1. **State the problem:** Multiply the expression $$\frac{1}{2}(-8y - 4)$$. 2. **Formula and rules:** When multiplying a fraction by a sum, distribute the fraction to each term ins

1. **State the problem:** Solve the equation $$7x - 4 - 6x - 14 = 30$$. 2. **Combine like terms:** Group the terms with $x$ and the constants.

1. **Statement of the problem:** We have the function $$f(x) = \frac{1}{6}x^3 - x^2$$ defined on $$\mathbb{R}$$.

1. **State the problem:** Solve the equation $$(3x - 1)^2 - (5x - 3)^2 = (4x - 2)^2$$ for $x$. 2. **Recall the formula:** This is a difference of squares on the left side: $$a^2 -

1. **Nyatakan masalah:** Kita diberikan persamaan beda linear homogen orde dua: $$y(k+2) - 8y(k+1) + 16y(k) = 0$$

1. **State the problem:** Solve for $x$ in the equation $$\frac{3x - 3}{5} = \frac{2x - 2}{4}$$ using cross multiplication. 2. **Formula and rule:** Cross multiplication means mult

1. **Énoncé du problème** : On considère la fonction $f$ définie par $f(x) = 0,05(x - 12)(x + 18)$ avec $\mathrm{dom}\,f = \mathbb{R}$. Il faut déterminer quelle affirmation parmi

1. The problem is to simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. The formula used here is to simplify fractions by factoring and canceling common factors.

1. The problem asks for the two double inequalities that define the shaded rectangular region bounded by vertical lines at $x=-3$ (dashed) and $x=2$ (solid), and horizontal lines a

1. **State the problem:** Simplify the fraction $\frac{25}{64}$. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their greatest common div

1. **Planteamiento del problema:** Tenemos un terreno rectangular de área total 8712 m² que debe dividirse en 3 parcelas iguales, cada una con área $\frac{8712}{3} = 2904$ m². 2. *