🧮 algebra

1. Problem: Construct a multiplication table modulo 9. 2. The multiplication modulo 9 means we multiply two numbers and then take the remainder when divided by 9.

1. **Problem Statement:** We need to define the piecewise function $E(d)$ that represents the down payment based on the number of units enrolled by a student. The units are integer

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation, multiply both sides by

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation, multiply both sides by

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve rational equations, multiply both sides by t

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor numerator and denominator

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Formula and rules:** To simplify a rational expression, factor numerator and denominator and cancel

1. **State the problem:** We are given the function $$f(-x) = \frac{4}{(-x)^2 + (-x) + 4}$$ and need to simplify it. 2. **Recall the rules:**

1. **State the problem:** Find the symmetry of the function $f(x) = \frac{x^2 - 4}{5 + x}$. 2. **Recall the rules for symmetry:**

1. **State the problem:** Simplify the expression $$\frac{3a^9 r^{-3}}{-4 (a^2)^{-1}}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{3b^{-9}}{(3b^{-4}c^{-3})^{-3}}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$\frac{x - 5}{7} = 40$$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 7 to eliminate the denomin

1. **State the problem:** Solve the equation $$\frac{w+7}{4} = \frac{w-5}{3}$$ for $w$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the leas

1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$y = -5x - 5$$ without graphing. 2. **Recall definitions:**

1. **State the problem:** Simplify the expression $$(3^2)^{-2}$$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents:

1. **State the problem:** Solve the system of equations by substitution: $$y = 2x - 13$$

1. **State the problem:** Evaluate the expression $$-(2a)^2 + 1 + 3$$ for $$a = 2$$. 2. **Write the expression:** $$-(2a)^2 + 1 + 3$$.

1. Stating the problem: Solve the first equation $12x = 120$ for $x$. 2. Formula and rules: To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is

1. **State the problem:** Evaluate the expression $5 (y + 2) - 61$ for $y = 3$. 2. **Write the expression:**

1. **State the problem:** Simplify the expression $$6 \div 2 - \left(81 \div 3^2\right)$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and

1. The problem asks about the slope of vertical and horizontal lines. 2. The slope of a line is defined as the change in $y$ divided by the change in $x$, or $$m=\frac{\Delta y}{\D