🧮 algebra

1. The problem asks us to express the quadratic expression $$q + 12x - qx^2$$ in the form $$a - b(x - c)^2$$ where $$a$$, $$b$$, and $$c$$ are in terms of $$q$$. 2. Start with the

1. **State the problem:** Solve the inequality $$x - 15 \leq -6$$ for $$x$$. 2. **Formula and rules:** To solve inequalities, we isolate $$x$$ by performing inverse operations. Whe

1. **State the problem:** Solve the inequality $$\frac{x}{-9} \geq 3$$ for $x$ and simplify the answer. 2. **Recall the rule for inequalities:** When multiplying or dividing both s

1. **State the problem:** Determine which rule represents the relationship between MSU-Balindong Community High School and its School ID 600313. 2. **Understand the problem:** The

1. Stating the problem: Solve the equation $2x + 3 = 7$. 2. Use the formula for solving linear equations: isolate $x$ by performing inverse operations.

1. **Problem:** Graph the quadratic function $f(x) = 3x^2 + 6x + 1$ and determine its domain and range. 2. **Formula and rules:** The domain of any quadratic function is all real n

1. **Stating the problem:** John had $3x$ rabbits. He sold 8 rabbits to Alex and 5 rabbits to Joseph. After selling, he was left with 32 rabbits.

1. **State the problem:** We have the function $$f : x \mapsto \frac{2x}{x-6}$$ with $$x \neq 6$$.

1. **State the problem:** Solve the equation $2x + 3 = 7$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse oper

1. The problem is to create a math problem involving the word "sex" as part of a variable or context, not inappropriately. 2. Let's consider a problem involving the number of males

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equat

1. **Stating the problem:** We need to find the solution region for the system of inequalities:

1. **State the problem:** Determine the type of system and the number of solutions for the system of equations: $$2x + 3y = 9$$

1. The problem involves finding the missing numbers in a 4x3 grid of sequences, where each box contains a sequence with some blanks. 2. To solve this, we analyze each sequence to i

1. **State the problem:** We need to find the average wind speed affecting a plane flying from Orlando to London and back, given the plane's airspeed and the times for each leg.

1. **State the problem:** We have a rectangle 24 meters long and want to find its width such that its area equals the area of a square with 12-meter sides. 2. **Formula for area:**

1. **State the problem:** A couple traveled a total distance $D$ during a camping trip. They went one-third of the way by boat, 10 miles by foot, and one-sixth of the way by horse.

1. **State the problem:** Solve the equation $$\frac{12}{b} - 3 = \frac{6}{b} + 4$$ for $b$. 2. **Isolate terms with $b$:** Move all terms involving $b$ to one side and constants t

1. **State the problem:** We are given three functions: $$f(x) = 3x, \quad g(x) = x^2, \quad h(x) = 2x - 5$$

1. **State the problem:** Solve the equation $$7c + 3(c - 5) = 2(c + 3) - 14$$ for $c$. 2. **Expand both sides:**

1. **State the problem:** Solve the equation $$3(x + 7) - 2 = 4(x - 2)$$ for $x$. 2. **Apply the distributive property:**