🧮 algebra

1. **State the problem:** If $x+2=4$, find the value of $x$. 2. **Use the subtraction property of equality:** Subtract $2$ from both sides to isolate $x$.

1. **State the problem:** Solve the system of equations: $$\frac{y}{2} - \frac{y+1}{3} = 0$$

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **State the problem:** Solve the equation $6x = 18 + 4x$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one side by perf

1. **State the problem:** Maria has only nickels and dimes, totaling 20 coins, worth 165 cents. Find the number of dimes. 2. **Define variables:** Let $n$ = number of nickels, $d$

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -3]$. 2. **Formula:** The average rate of change of a function $f(

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **Problem:** Sarah earned 3 more than double Eric's earnings. The difference is 15. Find their earnings. 2. **Formula:** Let Eric's earnings be $x$. Then Sarah's earnings are $2

1. **State the problem:** Simplify the expression $$7x^3 + \frac{4}{x^5} - \frac{3}{\sqrt[3]{5x}} + \frac{7x^2}{3} - \sqrt[3]{5}.$$ 2. **Recall important rules:**

1. **State the problem:** A grocery store had 2,418 boxes of cereal on Monday. By Friday, customers had bought 1,146 boxes. The remaining boxes were organized on 24 shelves evenly.

1. **State the problem:** We are given a line with equation $y = ax + b$. We need to find the values of $a$ (slope) and $b$ (y-intercept).

1. **Problem:** Factor the polynomial $x^2 + 11x + 28$. 2. **Formula:** To factor a quadratic $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$.

1. Stating the problem: Solve the equation $$x^4 - 30x^2 + 125 = 0$$ for $x$. 2. Recognize this is a quartic equation but can be treated as a quadratic in terms of $x^2$.

1. Stát an fhadhb: Tá líne ar dheis agus ba mhaith linn a fháil amach cén fáth gur fána dhiúltach atá inti. 2. Foirmle fána líne: Má tá dhá phointe ar líne, $ (x_1, y_1) $ agus $ (

1. **State the problem:** Find the coordinates of points A and B where the line $2x + 3y - 6 = 0$ intersects the x-axis and y-axis respectively, and then find the area of triangle

1. The problem is to solve a math problem, but since no specific problem was given, let's solve a simple algebraic equation as an example: Solve for $x$ in the equation $2x + 3 = 7

1. **State the problem:** Solve the proportion $\frac{2}{r} = \frac{12}{18}$. 2. **Formula and rule:** To solve proportions of the form $\frac{a}{b} = \frac{c}{d}$, use cross multi

1. **State the problem:** Solve the equation $$\frac{3}{4} + \frac{x}{3} = 5 - \frac{7}{12}$$ for $x$. 2. **Rewrite the equation:** Combine the constants on the right side:

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** Write the expression $3(2 - i) + i(5 + 2i)$ in the form $x + yi$, where $x, y \in \mathbb{R}$. 2. **Apply distributive property:**